MCQOPTIONS
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MCQOPTIONS
This section includes 12583 Mcqs, each offering curated multiple-choice questions to sharpen your Joint Entrance Exam - Main (JEE Main) knowledge and support exam preparation. Choose a topic below to get started.
| 1951. |
The displacement-time graphs of two particles A and B are straight lines making angles of \[30{}^\circ \] and \[60{}^\circ \] respectively with the time axis. If the velocity of A is \[{{v}_{A}}\] and that of B is \[{{v}_{B}}\], the value of \[{{v}_{A}}/{{v}_{B}}\] is |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{1}{\sqrt{3}}\] |
| C. | \[\sqrt{3}\] |
| D. | \[\frac{1}{3}\] |
| Answer» E. | |
| 1952. |
From a building two balls A and B are thrown such that A is thrown upwards and B downwards (both vertically). If \[{{v}_{A}}\] and \[{{v}_{B}}\] are their respective velocities on reaching the ground, then |
| A. | \[{{v}_{B}}>{{v}_{A}}\] |
| B. | \[{{v}_{A}}={{v}_{B}}\] |
| C. | \[{{v}_{A}}>{{v}_{B}}\] |
| D. | their velocities depend on their masses. |
| Answer» C. \[{{v}_{A}}>{{v}_{B}}\] | |
| 1953. |
A body starts from rest and travels 's' m in 2nd second, then acceleration is |
| A. | \[(2s)\text{ }m/{{s}^{2}}\] |
| B. | \[(3s)\text{ }m/{{s}^{2}}\] |
| C. | \[\left( \frac{2}{3}s \right)m/{{s}^{2}}\] |
| D. | \[\left( \frac{3}{2}s \right)m/{{s}^{2}}\] |
| Answer» D. \[\left( \frac{3}{2}s \right)m/{{s}^{2}}\] | |
| 1954. |
The angle which the velocity vector of a projectile thrown with a velocity v at an angle \[\theta \] to the horizontal will make with the horizontal after time t of its being thrown up is: |
| A. | \[\theta \] |
| B. | \[{{\tan }^{-1}}\left( \theta /\text{t} \right)\] |
| C. | \[{{\tan }^{-1}}\left( \frac{\text{v cos}\theta }{\text{v sin}\theta -\text{gt}} \right)\] |
| D. | \[{{\tan }^{-1}}\left( \frac{\text{v sin}\theta -\text{gt}}{\text{v cos}\theta } \right)\] |
| Answer» E. | |
| 1955. |
Two boats A and B, move away from a buoy anchored at the middle of a river along the mutually perpendicular straight lines: the boat A along the river and the boat B across the river. Having moved off an equal distance from the buoy the boat returned. What is the ratio of times of motion of boats \[\frac{{{\tau }_{A}}}{{{\tau }_{B}}},\] if the velocity of each boat with respect to water is 1.2 times greater than the stream velocity? |
| A. | 2.3 |
| B. | 1.8 |
| C. | 0.5 |
| D. | 0.2 |
| Answer» C. 0.5 | |
| 1956. |
A 2 m wide truck is moving with a uniform speed \[{{\text{v}}_{\text{0}}}\text{= 8 m/s}\] along a straight horizontal road. A pedestrain starts to cross the road with a uniform speed v when the truck is 4 m away from him. The minimum value of v so that he can cross the road safely is |
| A. | 2.62 m/s |
| B. | 4.6 m/s |
| C. | 3.57 m/s |
| D. | 1.414 m/s |
| Answer» D. 1.414 m/s | |
| 1957. |
Rain, pouring down at an angle\[\alpha \]with the vertical has a speed of \[10\text{ m}{{\text{s}}^{-1}}.\] A girl runs against the rain with a speed of \[\text{8 m}{{\text{s}}^{-1}}\] and sees that the rain makes an angle \[\beta \] with the vertical, then relation between \[\alpha \] and \[\beta \] is |
| A. | \[\tan \alpha =\frac{8+10\sin \beta }{10\cos \beta }\] |
| B. | \[\tan \beta =\frac{8+10\sin \alpha }{10\cos \alpha }\] |
| C. | \[\tan \alpha =\tan \beta \] |
| D. | \[\tan \alpha =\cot \beta \] |
| Answer» C. \[\tan \alpha =\tan \beta \] | |
| 1958. |
A man in a row boat must get from point A to point B on the opposite bank of the river (see figure). The distance\[BC=\text{ }a\]. The width of the river\[AC=b\]. At what minimum speed u relative to the still water should the boat travel to reach the point B? The velocity of flow of the river is \[{{v}_{0}}\]. |
| A. | \[\sqrt{{{\text{a}}^{2}}\text{+}{{\text{b}}^{2}}}/{{\text{v}}_{0}}\] |
| B. | \[\frac{{{\text{v}}_{0}}\text{b}}{\sqrt{{{\text{a}}^{2}}\text{+}{{\text{b}}^{2}}}}\] |
| C. | \[{{\text{v}}_{0}}\,\text{a/b}\] |
| D. | \[{{\text{v}}_{0}}\,\text{b/a}\] |
| Answer» C. \[{{\text{v}}_{0}}\,\text{a/b}\] | |
| 1959. |
A particle moves in a circle of radius 30 cm. Its linear speed is given by: \[V=2t\], where t in second and v in m/s. Find out its radial and tangential acceleration at t = 3 sec respectively. |
| A. | \[\text{220 m/se}{{\text{c}}^{\text{2}}}\text{, 50 m/se}{{\text{c}}^{\text{2}}}\] |
| B. | \[\text{110 m/se}{{\text{c}}^{\text{2}}}\text{, 5 m/se}{{\text{c}}^{\text{2}}}\] |
| C. | \[\text{120 m/se}{{\text{c}}^{\text{2}}}\text{, 2 m/se}{{\text{c}}^{\text{2}}}\] |
| D. | \[\text{110 m/se}{{\text{c}}^{\text{2}}}\text{, 10 m/se}{{\text{c}}^{\text{2}}}\] |
| Answer» D. \[\text{110 m/se}{{\text{c}}^{\text{2}}}\text{, 10 m/se}{{\text{c}}^{\text{2}}}\] | |
| 1960. |
A stone tied to the end of a string of 1 m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolution in 44 seconds, what is the magnitude and direction of acceleration of the stone? |
| A. | \[{{\pi }^{2}}\text{m}{{\text{s}}^{-2}}\] and direction along the radius towards the center. |
| B. | \[{{\pi }^{2}}\text{m}{{\text{s}}^{-2}}\] and direction along the radius away from the center. |
| C. | \[{{\pi }^{2}}\text{m}{{\text{s}}^{-2}}\] and direction along the tangent to the circle. |
| D. | \[{{\pi }^{2}}\text{/4m}{{\text{s}}^{-2}}\] and direction along the radius towards the center. |
| Answer» B. \[{{\pi }^{2}}\text{m}{{\text{s}}^{-2}}\] and direction along the radius away from the center. | |
| 1961. |
A cricket ball is hit with a velocity \[25\text{ }m{{s}^{-1}}\], \[60{}^\circ \] above the horizontal. How far above the ground, ball passes over a fielder 50 m from the bat (consider the ball is struck very close to the ground)? Take \[\sqrt{3}=\text{1}\text{.7 }\]and \[\text{g = 10 m}{{\text{s}}^{-2}}\] |
| A. | 6.8 m |
| B. | 7 m |
| C. | 5 m |
| D. | 10 m |
| Answer» D. 10 m | |
| 1962. |
Two particles A and B separated by a distance 2R are moving counter clockwise along the same circular path of radius R each with uniform speed v. At time \[t=0\], A is given a tangential acceleration of magnitude \[\alpha =\frac{\text{77}{{\text{v}}^{2}}}{25\pi \text{R}}\] then |
| A. | the time lapse for the two bodies to collide is \[\frac{6\pi \text{R}}{5\text{v}}\] |
| B. | the angle covered by A is 11\[\pi \]/6 |
| C. | angular velocity of A is \[\frac{11\text{v}}{5\text{R}}\] |
| D. | radial acceleration of A is \[\text{289 }{{\text{v}}^{\text{2}}}\text{/5R}\] |
| Answer» C. angular velocity of A is \[\frac{11\text{v}}{5\text{R}}\] | |
| 1963. |
A boat B is moving upstream with velocity 3 m/s with respect to ground. An observer standing on boat observes that a swimmer S is crossing the river perpendicular to the direction of motion of boat. If river flow velocity is 4 m/s and swimmer crosses the river of width 100 m in 50 sec, then |
| A. | velocity of swimmer w.r.t ground is \[\surd 13\,\,m\text{/}s\] |
| B. | drift of swimmer along river is zero |
| C. | drift of swimmer along river will be 50 m |
| D. | velocity of swimmer w.r.t ground is 2 m/s |
| Answer» B. drift of swimmer along river is zero | |
| 1964. |
An aircraft executes a horizontal loop of radius km with a steady speed of \[900\text{ }km/h\]. The ratio of centripetal acceleration to acceleration due to gravity is \[\left[ \text{g = 9}\text{.8 m/}{{\text{s}}^{\text{2}}} \right]\] |
| A. | 6.38 |
| B. | 9.98 |
| C. | 11.33 |
| D. | 12.13 |
| Answer» B. 9.98 | |
| 1965. |
If \[{{\text{V}}_{\text{r}}}\] is the velocity of rain falling vertically and \[{{\text{V}}_{\text{m}}}\] is the velocity of a man walking on a level road, and \[\theta \] is the angle with vertical at which he should hold the umbrella to protect himself than the relative velocity of rain w.r.t. the man is given by: |
| A. | \[{{\text{V}}_{\text{r}\,\text{m}}}=\sqrt{{{\text{V}}_{r}}^{2}+{{\text{V}}_{\text{m}}}^{2}+2{{\text{V}}_{r}}{{\text{V}}_{\text{m}}}\cos \theta }\] |
| B. | \[{{\text{V}}_{\text{r}\,\text{m}}}=\sqrt{{{\text{V}}_{r}}^{2}+{{\text{V}}_{\text{m}}}^{2}-2{{\text{V}}_{r}}{{\text{V}}_{\text{m}}}\cos \theta }\] |
| C. | \[{{\text{V}}_{\text{r}\,\text{m}}}=\sqrt{{{\text{V}}_{r}}^{2}+{{\text{V}}_{\text{m}}}^{2}}\] |
| D. | \[{{\text{V}}_{\text{r}\,\text{m}}}=\sqrt{{{\text{V}}_{r}}^{2}-{{\text{V}}_{\text{m}}}^{2}}\] |
| Answer» D. \[{{\text{V}}_{\text{r}\,\text{m}}}=\sqrt{{{\text{V}}_{r}}^{2}-{{\text{V}}_{\text{m}}}^{2}}\] | |
| 1966. |
A boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water in \[km/hr\,\]is |
| A. | 3 |
| B. | 4 |
| C. | \[\sqrt{21}\] |
| D. | 1 |
| Answer» B. 4 | |
| 1967. |
It was calculated that a shell when fired from a gun with a certain velocity and at an angle of elevation \[5\pi /36\] rad should strike a given target. In actual practice, it was found that a hill just prevented the trajectory. At what angle (rad) of elevation should the gun be fired to hit the target |
| A. | \[\frac{5\pi }{36}\] |
| B. | \[\frac{11\pi }{36}\] |
| C. | \[\frac{7\pi }{36}\] |
| D. | \[\frac{13\pi }{36}\] |
| Answer» E. | |
| 1968. |
A boat is moving with a velocity \[3\text{ }\hat{i}+4\text{ \hat{j}}\] with respect to ground. The water in the river is moving with a velocity \[-3\text{ }\hat{i}-4\text{ \hat{j}}\] with respect to ground. The relative velocity of the boat with respect to water is |
| A. | \[8\hat{j}\] |
| B. | \[-6\hat{i}-8\hat{j}\] |
| C. | \[6\hat{i}+8\hat{j}\] |
| D. | \[5\sqrt{2}\] |
| Answer» D. \[5\sqrt{2}\] | |
| 1969. |
A boy is standing on a cart moving along x-axis with the speed of 10 m/s. When the cart reaches the origin he throws a stone in the horizontal x-y plane with the speed of 5 m/s with respect to himself at an angle \[\theta \] with the x-axis. It is found that the stone hits a ball lying at rest at a point whose co-ordinates are\[\left( \sqrt{3}\,m,\text{ }1\,m \right)\]. The value of \[\theta \] is (gravitational effect is to be ignored) |
| A. | \[30{}^\circ \] |
| B. | \[60{}^\circ \] |
| C. | \[90{}^\circ \] |
| D. | \[120{}^\circ \] |
| Answer» B. \[60{}^\circ \] | |
| 1970. |
A projectile is fired with a velocity v at right angle to the slope which is inclined at an angle \[\theta \] with the horizontal. The range of the projectile along the inclined plane is: |
| A. | \[\frac{2{{\text{v}}^{\text{2}}}\tan \theta }{\text{g}}\] |
| B. | \[\frac{{{\text{v}}^{\text{2}}}\sec \theta }{\text{g}}\] |
| C. | \[\frac{2{{\text{v}}^{\text{2}}}\tan \theta \sec \theta }{\text{g}}\] |
| D. | \[\frac{{{\text{v}}^{\text{2}}}sin\theta }{\text{g}}\] |
| Answer» D. \[\frac{{{\text{v}}^{\text{2}}}sin\theta }{\text{g}}\] | |
| 1971. |
Three particles A, B and C are thrown from the top of a tower with the same speed. A is thrown up, B is thrown down and C is horizontally. They hit the ground with speeds \[{{\text{v}}_{\text{A}}}\], \[{{\text{v}}_{\text{B}}}\] and \[{{\text{v}}_{\text{C}}}\] respectively then, |
| A. | \[{{\text{v}}_{\text{A}}}\text{=}{{\text{v}}_{\text{B}}}\text{=}{{\text{v}}_{\text{C}}}\] |
| B. | \[{{\text{v}}_{\text{A}}}\text{=}{{\text{v}}_{\text{B}}}\text{}{{\text{v}}_{\text{C}}}\] |
| C. | \[{{\text{v}}_{\text{A}}}\text{}{{\text{v}}_{\text{C}}}\text{}{{\text{v}}_{\text{B}}}\] |
| D. | \[{{\text{v}}_{\text{A}}}\text{}{{\text{v}}_{\text{B}}}\text{=}{{\text{v}}_{\text{C}}}\] |
| Answer» B. \[{{\text{v}}_{\text{A}}}\text{=}{{\text{v}}_{\text{B}}}\text{}{{\text{v}}_{\text{C}}}\] | |
| 1972. |
A body is thrown horizontally with a velocity \[\sqrt{2gh}\] from the top of a tower of height h. It strikes the level ground through the foot of the tower at a distance x from the tower. The value of x is |
| A. | \[h\] |
| B. | \[h/2\] |
| C. | \[~2h~\] |
| D. | \[2h/3\] |
| Answer» D. \[2h/3\] | |
| 1973. |
A large number of bullets are fired in all directions with the same speed v. What is the maximum area on the ground on which these bullets will spread? |
| A. | \[\frac{\pi {{\text{v}}^{2}}}{\text{g}}\] |
| B. | \[\frac{\pi {{\text{v}}^{4}}}{{{\text{g}}^{2}}}\] |
| C. | \[{{\pi }^{2}}\frac{{{\text{v}}^{2}}}{{{\text{g}}^{2}}}\] |
| D. | \[\frac{{{\pi }^{2}}{{\text{v}}^{4}}}{{{\text{g}}^{2}}}\] |
| Answer» C. \[{{\pi }^{2}}\frac{{{\text{v}}^{2}}}{{{\text{g}}^{2}}}\] | |
| 1974. |
A particle P is projected from a point on the surface of smooth inclined plane (see figure). Simultaneously another particle Q is released on the smooth inclined plane from the same position. P and Q collide on the inclined plane after \[t=4\] second. The speed of projection of P is |
| A. | 5 m/s |
| B. | 10 m/s |
| C. | 15 m/s |
| D. | 20 m/s |
| Answer» C. 15 m/s | |
| 1975. |
For an observer on trolley direction of projection of particle is shown in the figure, while for observer on ground ball rise vertically. The maximum height reached by ball from trolley is |
| A. | 10 m |
| B. | 15 m |
| C. | 20 m |
| D. | 5 m |
| Answer» C. 20 m | |
| 1976. |
The position of a projectile launched from the origin at \[t=0\]is given by \[\vec{r}=(40\hat{i}+50\hat{j})m\] at 2s. If the projectile was launched at an angle \[\theta \] from the horizontal, then \[\theta \] is (take \[\text{g = 10 m}{{\text{s}}^{-2}}\]) |
| A. | \[{{\tan }^{-1}}\frac{2}{3}\] |
| B. | \[{{\tan }^{-1}}\frac{3}{2}\] |
| C. | \[{{\tan }^{-1}}\frac{7}{4}\] |
| D. | \[{{\tan }^{-1}}\frac{4}{5}\] |
| Answer» D. \[{{\tan }^{-1}}\frac{4}{5}\] | |
| 1977. |
A particle is projected from a tower as shown in figure, then the distance from the foot of the tower where it will strike the ground will be |
| A. | 4000/3 m |
| B. | 2000/m |
| C. | 1000/3 m |
| D. | 2500/3 m |
| Answer» B. 2000/m | |
| 1978. |
An object is projected with a velocity of \[20\text{ }m/s\] making an angle of \[45{}^\circ \] with horizontal. The equation for the trajectory is \[h=Ax-B{{x}^{2}}\] where h is height, x is horizontal distance, A and B are constants. The ratio A: B is \[\left( \text{g = 10 m}{{\text{s}}^{-2}} \right)\] |
| A. | \[1\text{ }:\text{ }5\] |
| B. | \[5\text{ }:\text{ }1~~\] |
| C. | \[1\text{ }:\text{ }40\] |
| D. | \[40\text{ }:\text{ }1\] |
| Answer» E. | |
| 1979. |
A jet plane flying at a constant velocity v at a height \[h=8\text{ }km\], is being tracked by a radar R located at O directly below the line of flight. If the angle \[\theta \] is decreasing at the rate of \[0.025\text{ }rad/s\], the velocity of the plane when \[\theta =\text{ }60{}^\circ \]is: |
| A. | 1440 km/h |
| B. | 960 km/h |
| C. | 1920 km/h |
| D. | 480 km/h |
| Answer» C. 1920 km/h | |
| 1980. |
A body is thrown with a velocity of \[9.8\text{ }m{{s}^{-1}}\] making an angle of \[30{}^\circ \] with the horizontal. It will hit the ground after a time |
| A. | 3.0 s |
| B. | 2.0 s |
| C. | 1.5 s |
| D. | 1 s |
| Answer» E. | |
| 1981. |
You throw a ball with a \[\text{\vec{v}}=\left( 3\hat{i}+4\hat{j} \right)\,\,\text{m/s}\] towards a wall, where it hits at height \[{{h}_{1}}\]. Suppose that the launch velocity were, instead, \[\text{\vec{v}}=\left( 5\hat{i}+4\hat{j} \right)\text{m/s}\] and \[{{h}_{2}}\] is height, then |
| A. | \[{{\text{h}}_{\text{1}}}\text{=}{{\text{h}}_{\text{2}}}\] |
| B. | \[{{\text{h}}_{\text{2}}}\text{}{{\text{h}}_{\text{1}}}\] |
| C. | \[{{\text{h}}_{\text{2}}}\text{}{{\text{h}}_{1}}\] |
| D. | \[{{\text{h}}_{\text{2}}}\ge {{\text{h}}_{\text{1}}}\] |
| Answer» C. \[{{\text{h}}_{\text{2}}}\text{}{{\text{h}}_{1}}\] | |
| 1982. |
For a stone thrown from a lower of unknown height, the maximum range for a projection speed of 10 m/s is obtained for a projection angle of \[30{}^\circ .\] The corresponding distance between the foot of the lower and the point of landing of the stone is |
| A. | \[10\text{ }m\] |
| B. | \[~20\text{ }m\] |
| C. | \[\left( \text{20/}\sqrt{3} \right)\text{ m }\!\!~\!\!\text{ }\] |
| D. | \[\left( 10/\sqrt{3} \right)\text{ m}\] |
| Answer» E. | |
| 1983. |
If retardation produced by air resistance of projectile is one-tenth of acceleration due to gravity, the time to reach maximum height |
| A. | decreases by 11 percent |
| B. | increases by 11 percent |
| C. | decreases by 9 percent |
| D. | increases by 9 percent |
| Answer» D. increases by 9 percent | |
| 1984. |
A particle is projected with a certain velocity at an angle \[\alpha \] above the horizontal from the foot of an inclined plane of inclination \[30{}^\circ \]. If the particle strikes the plane normally then a is |
| A. | \[30{}^\circ +\text{ta}{{\text{n}}^{-1}}\left( \frac{\sqrt{3}}{2} \right)\] |
| B. | \[30{}^\circ +\text{ta}{{\text{n}}^{-1}}\left( \frac{1}{2} \right)\] |
| C. | \[30{}^\circ +\text{ta}{{\text{n}}^{-1}}1\] |
| D. | \[60{}^\circ \] |
| Answer» B. \[30{}^\circ +\text{ta}{{\text{n}}^{-1}}\left( \frac{1}{2} \right)\] | |
| 1985. |
An aircraft moving with a speed of 250 m/s is at a height of 6000 m, just overhead of an anti. Aircraft gun. If the muzzle velocity is 500 m/s, the firing angle q should be: |
| A. | \[30{}^\circ \] |
| B. | \[45{}^\circ \] |
| C. | \[60{}^\circ \] |
| D. | \[75{}^\circ \] |
| Answer» D. \[75{}^\circ \] | |
| 1986. |
A projectile of mass m is thrown with a velocity v making an angle \[60{}^\circ \] with the horizontal. Neglecting air resistance, the change in velocity from the departure A to its arrival at B, along the vertical direction is |
| A. | 2v |
| B. | \[\sqrt{3}\text{v}\] |
| C. | v |
| D. | \[\frac{\text{v}}{\sqrt{3}}\] |
| Answer» C. v | |
| 1987. |
A body of mass m is projected horizontally with a velocity v from the top of a tower of height h and it reaches the ground at a distance x from the foot of the tower. If a second body of mass 2m is projected horizontally from the top of a tower of height 2h, it reaches the ground at a distance 2x from the foot of the tower. The horizontal velocity of the second body is |
| A. | \[~v\] |
| B. | \[2v\] |
| C. | \[\sqrt{2v}\] |
| D. | \[v/2\] |
| Answer» D. \[v/2\] | |
| 1988. |
Two balls are projected at an angle \[\theta \] and \[(90{}^\circ -\theta )\] to the horizontal with the same speed. The ratio of their maximum vertical heights is B Tricky |
| A. | 1:1 |
| B. | \[\text{tan}\theta :1\] |
| C. | \[1:\text{tan}\theta \] |
| D. | \[\text{ta}{{\text{n}}^{2}}\theta :1\] |
| Answer» E. | |
| 1989. |
A ball rolls off to the top of a staircase with a horizontal velocity u m/s. If the steps are h meter high and b meter wide, the ball will hit the edge of the nth step, if |
| A. | \[n=\frac{2hu}{g{{b}^{2}}}\] |
| B. | \[n=\frac{2h{{u}^{2}}}{gb}\] |
| C. | \[n=\frac{2h{{u}^{2}}}{g{{b}^{2}}}\] |
| D. | \[n=\frac{h{{u}^{2}}}{g{{b}^{2}}}\] |
| Answer» D. \[n=\frac{h{{u}^{2}}}{g{{b}^{2}}}\] | |
| 1990. |
A projectile is thrown in the upward direction making an angle of \[60{}^\circ \] with the horizontal direction with a velocity of 147\[m{{s}^{-1}}\]. Then the time after which its inclination with the horizontal is \[45{}^\circ \], is |
| A. | \[15\left( \sqrt{3}-1 \right)\text{s}\] |
| B. | \[15\left( \sqrt{3}+1 \right)\text{s}\] |
| C. | \[7.5\left( \sqrt{3}-1 \right)\text{s}\] |
| D. | \[7.5\left( \sqrt{3}+1 \right)\text{s}\] |
| Answer» D. \[7.5\left( \sqrt{3}+1 \right)\text{s}\] | |
| 1991. |
A particle is projected at an angle of elevation \[\alpha \] and after t seconds it appears to have an angle of elevation \[\beta \] as seen from point of projection. The initial velocity will be |
| A. | \[\frac{gt}{2\sin \left( \alpha -\beta \right)}\] |
| B. | \[\frac{gt\,\cos \beta }{2\sin \left( \alpha -\beta \right)}\] |
| C. | \[\frac{\sin \left( \alpha -\beta \right)}{2gt}\] |
| D. | \[\frac{2\sin \left( \alpha -\beta \right)}{gt\,\cos \beta }\] |
| Answer» C. \[\frac{\sin \left( \alpha -\beta \right)}{2gt}\] | |
| 1992. |
A projectile is fired from the surface of the earth with a velocity of 5 \[m{{s}^{-1}}\,\] and angle \[\theta \] with the horizontal. Another projectile fired from another planet with a velocity of 3 \[m{{s}^{-1}}\,\]at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in \[\text{m}{{\text{s}}^{-2}}\]) given \[\text{g = 9}\text{.8 m/}{{\text{s}}^{\text{2}}}\] |
| A. | 3.5 |
| B. | 5.9 |
| C. | 163 |
| D. | 110.8 |
| Answer» B. 5.9 | |
| 1993. |
A particle is projected with a velocity v such that its range on the horizontal plane is twice the greatest height attained by it. The range of the projectile is (where g is acceleration due to gravity) |
| A. | \[\frac{4{{v}^{2}}}{5g}\] |
| B. | \[\frac{4g}{5{{v}^{2}}}\] |
| C. | \[\frac{{{v}^{2}}}{g}\] |
| D. | \[\frac{4{{v}^{2}}}{\sqrt{5}g}\] |
| Answer» B. \[\frac{4g}{5{{v}^{2}}}\] | |
| 1994. |
A body is projected vertically upwards with a velocity u, after time t another body is projected vertically upwards from the same point with a velocity v, where v < u. If they meet as soon as possible, then choose the correct option |
| A. | \[t=\frac{u-v+\sqrt{{{u}^{2}}+{{v}^{2}}}}{g}\] |
| B. | \[t=\frac{u-v+\sqrt{{{u}^{2}}-{{v}^{2}}}}{g}\] |
| C. | \[t=\frac{u+v+\sqrt{{{u}^{2}}-{{v}^{2}}}}{g}\] |
| D. | \[t=\frac{u-v+\sqrt{{{u}^{2}}-{{v}^{2}}}}{2g}\] |
| Answer» C. \[t=\frac{u+v+\sqrt{{{u}^{2}}-{{v}^{2}}}}{g}\] | |
| 1995. |
A projectile is given an initial velocity of \[\left( \hat{i}\text{ }+\text{ }2\text{ }\hat{j} \right)\text{ }m/s\], where; is along the ground and j is along the vertical. If \[g=10\text{ }m/{{s}^{2}}\], the equation of its trajectory is : |
| A. | \[y=x-5{{x}^{2}}\] |
| B. | \[y=2x-5{{x}^{2}}\] |
| C. | \[4y=2x-5{{x}^{2~}}~\] |
| D. | \[4y=2x-25{{x}^{2}}\] |
| Answer» C. \[4y=2x-5{{x}^{2~}}~\] | |
| 1996. |
A body projected at an angle with the horizontal has a range 300 m. If the time of flight is 6 s, then the horizontal component of velocity is |
| A. | \[30\text{ m}\,\,{{\text{s}}^{-1}}\] |
| B. | \[50\text{ m}\,\,{{\text{s}}^{-1}}\] |
| C. | \[40\text{ m}\,\,{{\text{s}}^{-1}}\] |
| D. | \[45\text{ m}\,\,{{\text{s}}^{-1}}\] |
| Answer» C. \[40\text{ m}\,\,{{\text{s}}^{-1}}\] | |
| 1997. |
Two pegs A and B thrown with speeds in the ratio 1:3 acquired the same heights. If A is thrown at an angle of \[30{}^\circ \] with the horizontal, the angle of projection of B will be |
| A. | \[0{}^\circ \] |
| B. | \[si{{n}^{-1}}\left( \frac{1}{8} \right)\] |
| C. | \[si{{n}^{-1}}\left( \frac{1}{6} \right)\] |
| D. | \[si{{n}^{-1}}\left( \frac{1}{2} \right)\] |
| Answer» D. \[si{{n}^{-1}}\left( \frac{1}{2} \right)\] | |
| 1998. |
A bullet is fired with a speed of \[1500\text{ }m\text{/}s\] in order to hit a target 100 m away. If \[g=10\text{ }m\text{/}{{s}^{2}}.\]The gun should be aimed |
| A. | 15 cm above the target |
| B. | 10 cm above the target |
| C. | 2.2 cm above the target |
| D. | directly towards the target |
| Answer» D. directly towards the target | |
| 1999. |
A projectile is thrown in the upward direction making an angle of \[\,60{}^\circ \] with the horizontal direction with a velocity of \[147\text{ }m{{s}^{-1}}\]. Then the time after which its inclination with the horizontal is \[45{}^\circ \], is |
| A. | 15 s |
| B. | 10.98 s |
| C. | 5.49 s |
| D. | 2.74 s |
| Answer» D. 2.74 s | |
| 2000. |
The equation of trajectory of projectile is given by\[y=\frac{x}{\sqrt{3}}-\frac{\text{g}{{\text{x}}^{2}}}{20}\], where x and y are in meter. The maximum range of the projectile is |
| A. | \[\frac{8}{3}\text{ m}\] |
| B. | \[\frac{4}{3}\text{ m}\] |
| C. | \[\frac{3}{4}\text{ m}\] |
| D. | \[\frac{3}{8}\text{ m}\] |
| Answer» C. \[\frac{3}{4}\text{ m}\] | |