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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.
| 5051. |
A particle is executing SHM according to the equation\[x=A\cos \omega t\]. Average speed of the particle during the interval\[0\le t\le \frac{\pi }{6\omega }\] |
| A. | \[\frac{\sqrt{3}A\omega }{2}\] |
| B. | \[\frac{\sqrt{3}A\omega }{4}\] |
| C. | \[\frac{3A\omega }{\pi }\] |
| D. | \[\frac{3A\omega }{\pi }(2-\sqrt{3})\] |
| Answer» E. | |
| 5052. |
The bob of a simple pendulum executes SHM in water with a period\[t\], while the period of oscillation of the bob is \[{{t}_{0}}\] in air. Neglecting the frictional force of water and given that the density of the bob is\[(4/3)\,\times 1000\,kg/{{m}^{3}}\]. What relationship between \[t\] and \[{{t}_{0}}\] is true? |
| A. | \[{{t}_{{}}}={{t}_{0}}\] |
| B. | \[{{t}_{{}}}=4{{t}_{0}}\] |
| C. | \[{{t}_{{}}}=2{{t}_{0}}\] |
| D. | \[{{t}_{{}}}={{t}_{0}}/2\] |
| Answer» D. \[{{t}_{{}}}={{t}_{0}}/2\] | |
| 5053. |
From the variation of potential energy in the direction of small oscillation of a simple pendulum, find the effective spring constant for the simple pendulum, where m is mass of the bob, \[l\] is length of the simple pendulum. |
| A. | \[\frac{mg}{l}\] |
| B. | \[\frac{mg}{2l}\] |
| C. | \[\frac{2mg}{l}\] |
| D. | \[\frac{mg}{\sqrt{2}l}\] |
| Answer» B. \[\frac{mg}{2l}\] | |
| 5054. |
A particle of mass m is executing oscillations about the origin on the.\[Y\]-axis with amplitude\[A\].Its potential energy is given as\[U(x)=b{{x}^{4}}\], where \[\beta \] is a positive constant. The \[x\]-coordinate of the particle, where the potential energy is one-third of the kinetic energy, is |
| A. | \[\pm \frac{A}{2}\] |
| B. | \[\pm \frac{A}{\sqrt{2}}\] |
| C. | \[\pm \frac{A}{3}\] |
| D. | \[\pm \frac{A}{\sqrt{3}}\] |
| Answer» C. \[\pm \frac{A}{3}\] | |
| 5055. |
A particle moves along a straight line to follow the equation\[a{{x}^{2}}+b{{v}^{2}}=k\], where\[a\], \[b\] and k are constants and \[x\] and \[v\] are x-coordinate and velocity of the particle respectively. Find the amplitude. |
| A. | \[\sqrt{\frac{k}{b}}\] |
| B. | \[\sqrt{\frac{b}{k}}\] |
| C. | \[\sqrt{\frac{a}{k}}\] |
| D. | \[\sqrt{\frac{k}{a}}\] |
| Answer» E. | |
| 5056. |
One end of a spring of force constant \[k\] is fixed to a vertical wall and the other to a body of mass \[m\] resting on a smooth horizontal surface. There is another wall at a distance \[{{x}_{0}}\] from the body. The spring is then compressed by 3\[{{x}_{0}}\] and released. The time taken to strike the wall from the instant of release is (given\[{{\sin }^{-1}}(1/3)=(\pi /9))\] |
| A. | \[\frac{\pi }{6}\sqrt{\frac{m}{k}}\] |
| B. | \[\frac{2\pi }{3}\sqrt{\frac{m}{k}}\] |
| C. | \[\frac{\pi }{4}\sqrt{\frac{m}{k}}\] |
| D. | \[\frac{11\pi }{9}\sqrt{\frac{m}{k}}\] |
| Answer» E. | |
| 5057. |
A particle is subjected to two simple harmonic motions in the same direction having equal amplitude and equal frequency. If the resultant amplitude is equal to the amplitude of the individual motions, what is the phase difference between the two simple harmonic motions? |
| A. | \[\frac{2\pi }{3}\] |
| B. | \[\frac{\pi }{3}\] |
| C. | \[\frac{\pi }{\sqrt{3}}\] |
| D. | \[\frac{2\pi }{\sqrt{3}}\] |
| Answer» B. \[\frac{\pi }{3}\] | |
| 5058. |
A cylindrical piston of mass M slides smoothly inside a long cylinder closed at one end, enclosing a certain mass of gas. The cylinder is kept with its axis horizontal. If the piston is disturbed from its equilibrium position, it oscillates simple harmonically. The period of oscillation will be |
| A. | \[T=2\pi \sqrt{\left( \frac{Mh}{PA} \right)}\] |
| B. | \[T=2\pi \sqrt{\left( \frac{Mh}{Ph} \right)}\] |
| C. | \[T=2\pi \sqrt{\left( \frac{M}{PAh} \right)}\] |
| D. | \[T=2\pi \sqrt{MPhA}\] |
| Answer» B. \[T=2\pi \sqrt{\left( \frac{Mh}{Ph} \right)}\] | |
| 5059. |
A mass of 1 kg is suspended by a string A. Another string C is connected to its lower end. If a sudden jerk is given to C, then |
| A. | the portion AB of the string will break |
| B. | the portion BC of the string will break |
| C. | none of the strings will break |
| D. | the mass will start rotating |
| Answer» C. none of the strings will break | |
| 5060. |
A block is lying on the horizontal frictionless surface. One end of a uniform rope is fixed to the block which is pulled in the horizontal direction by applying a force F at the other end. If the mass of the rope is half the mass of the block, the tension in the middle of the rope will be |
| A. | \[F\] |
| B. | \[2\,F/3\] |
| C. | \[3\,F/5\] |
| D. | \[5\,F/6\] |
| Answer» E. | |
| 5061. |
Two wooden blocks are moving on a smooth horizontal surface such that the mass \[m\] remains stationary with respect to the block of mass M as shown in the figure. The magnitude of force \[p\]is |
| A. | \[(M+m)g\,tan\,\beta \] |
| B. | \[g\,\tan \,\beta \] |
| C. | \[mg\,\cos \,\beta \] |
| D. | \[(M+m)g\,\cos ec\,\beta \] |
| Answer» B. \[g\,\tan \,\beta \] | |
| 5062. |
A 15 kg block is initially moving along a smooth horizontal surface with a speed of \[v=4\,m/s\] to the left. It is acted by a force \[F\], which varies in the manner shown. Determine the velocity of the block at \[t=15\] seconds. Given that, \[F=40\cos \left( \frac{\pi }{10} \right)t\] |
| A. | 12.5 m/s |
| B. | 8.5 m/s |
| C. | 20 m/s |
| D. | 9.5 m/s |
| Answer» B. 8.5 m/s | |
| 5063. |
An object is suspended from a spring balance in a lift. The reading is 240 N when the lift is at rest. If the spring balance reading now changes to 220 N, then the lift is moving |
| A. | Downward with constant speed |
| B. | Downward with decreasing speed |
| C. | Downward with increasing speed |
| D. | Upward with increasing speed |
| Answer» D. Upward with increasing speed | |
| 5064. |
Initially the spring is undeformed. Now the force \[F\] is applied to \[B\] as shown in the figure. When the displacement of \[B\] w.r.t. \[A\] is x towards right in some time then the relative acceleration of \[B\] w.r.t. \[A\] at that moment is |
| A. | \[\frac{F}{2m}\] |
| B. | \[\frac{F-kx}{m}\] |
| C. | \[\frac{F-2kx}{m}\] |
| D. | None of these |
| Answer» D. None of these | |
| 5065. |
A light spring balance hangs from the hook of the other light spring balance and a block of mass M kilogram hangs from the former one. Which of the following statements about the scale reading is true? |
| A. | Both the scales read \[M/2\] kilogram each. |
| B. | Both the scales read \[M\] kilogram each. |
| C. | The scale of the lower one reads \[M\] kilogram and of the upper one zero. |
| D. | The reading of the two scales can be anything but the sum of the reading will be \[M\] kilogram. |
| Answer» C. The scale of the lower one reads \[M\] kilogram and of the upper one zero. | |
| 5066. |
The system starts from rest and \[A\] attains a velocity of 5 m/s after it has moved 5 m towards right. Assuming the arrangement to be frictionless everywhere and pulley and strings to be light, the value of the constant force \[F\] applied on A is |
| A. | 50 N |
| B. | 75 N |
| C. | 100 N |
| D. | 96 N |
| Answer» C. 100 N | |
| 5067. |
A light string passing over a smooth light pulley connects two blocks of masses \[{{m}_{1}}\] and \[{{m}_{2}}\] (vertically). If the acceleration of the system is g/8, then the ratio of the masses is |
| A. | 8 : 1 |
| B. | 0.379861111111111 |
| C. | 4 : 3 |
| D. | 0.210416666666667 |
| Answer» C. 4 : 3 | |
| 5068. |
A bead of mass m is attached to one end of a spring of natural length R and spring constant\[k=\frac{(\sqrt{3}+1)mg}{R}\] The other end of the spring is fixed at a point A on a smooth vertical ring of radius R as shown in the figure. The normal reaction at B just after it is released to move is |
| A. | \[mg/2\] |
| B. | \[\sqrt{3\,}mg\] |
| C. | \[3\sqrt{3\,}mg\] |
| D. | \[\frac{3\sqrt{3}mg}{2}\] |
| Answer» E. | |
| 5069. |
A wooden box is placed on a table. The normal force on the box from the table is A \[{{N}_{1}}\]. Now another identical box is kept on first box and the normal force on lower block due to upper block is A\[{{N}_{2}}\] and normal force on lower block by the table is \[{{N}_{3}}\]. For this situation, mark out the correct statement(s). |
| A. | \[{{N}_{1}}={{N}_{2}}={{N}_{3}}\] |
| B. | \[{{N}_{1}}<{{N}_{2}}={{N}_{3}}\] |
| C. | \[{{N}_{1}}={{N}_{2}}>{{N}_{3}}\] |
| D. | None of these |
| Answer» E. | |
| 5070. |
Two identical small masses each of mass m are connected by a light inextensible string on a smooth m horizontal floor. A constant force F is applied t at the mid point of the string as shown in the figure. The acceleration of each mass 1 towards each other is, |
| A. | \[\frac{F}{2\sqrt{3m}}\] |
| B. | \[\frac{\sqrt{3}F}{2m}\] |
| C. | \[\frac{2}{\sqrt{3}}\,\frac{F}{m}\] |
| D. | None of these |
| Answer» B. \[\frac{\sqrt{3}F}{2m}\] | |
| 5071. |
A U-shaped wire has a rough semicircular bending between \[A\] and \[B\] as shown in the figure. \[A\] bead of mass m moving with uniform speed \[v\] through the wire enters the semicircular bend at \[A\] and leaves at \[B\] with velocity \[v/2\]after time \[T\]. The average force, exerted by the bead on the part \[A\]\[B\] of the wire is |
| A. | \[\frac{mv}{2T}\] |
| B. | \[\frac{3mv}{2T}\] |
| C. | \[\frac{3mv}{T}\] |
| D. | None of these |
| Answer» C. \[\frac{3mv}{T}\] | |
| 5072. |
The force required just to move a body up an inclined plane is double the force required just to prevent the body sliding down. If the coefficient of friction is 0.25, the angle of inclination of the plane is |
| A. | \[37{}^\circ \] |
| B. | \[45{}^\circ \] |
| C. | \[30{}^\circ \] |
| D. | \[~53{}^\circ \] |
| Answer» B. \[45{}^\circ \] | |
| 5073. |
A circular road of radius R is banked for a speed v = 40 km/hr. A car of mass m attempts to go on the circular road, the friction co-efficient between the tyre and road is negligible: |
| A. | the car cannot make a turn without skidding |
| B. | if the car runs at a speed less than 40 km/hr, it will slip up the slope |
| C. | if the car runs at the correct speed of 40 km/hr, the force by the road on the car is equal to \[m{{v}^{2}}/r\] |
| D. | if the car runs at the correct speed of 40 km/hr, the force by the road on the car is greater than mg as well as greater than \[m{{v}^{2}}/r\] |
| Answer» E. | |
| 5074. |
A coin is placed at the edge of a horizontal disc rotating about a vertical axis through its axis with a uniform angular speed 2 rad \[{{s}^{-1}}\]. The radius of the disc is 50 cm. Find the minimum coefficient of friction between disc and coin so that the coin does not slip \[(g=10m{{s}^{-2}})\]. |
| A. | 0.1 |
| B. | 0.2 |
| C. | 0.3 |
| D. | 0.4 |
| Answer» C. 0.3 | |
| 5075. |
A house is built on the top of a hill with \[45{}^\circ \] slope. Due to the sliding of material and sand from top to the bottom of hill, the slope angle has been reduced. If the coefficient of static friction Between sand particles is 0.75, what is the final angle attained by hill? \[(ta{{n}^{-1}}0.75\simeq {{37}^{0}})\] |
| A. | \[8{}^\circ \] |
| B. | \[~45{}^\circ \] |
| C. | \[37{}^\circ \] |
| D. | \[30{}^\circ \] |
| Answer» D. \[30{}^\circ \] | |
| 5076. |
A block of mass m is at rest with respect to a rough incline kept in elevator moving up With acceleration a. Which of following statements is correct? |
| A. | The contact force between block and incline is parallel to the incline. |
| B. | The contact force between block and incline is of the magnitude \[m(g+a)\]. |
| C. | The contact force between block and incline is perpendicular to the incline. |
| D. | The contact force is of the magnitude \[mg\,cos\,\theta \] |
| Answer» C. The contact force between block and incline is perpendicular to the incline. | |
| 5077. |
The upper half of an inclined plane with inclination \[\phi \] is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by |
| A. | \[2\,\tan \,\phi \] |
| B. | \[\,\tan \,\phi \] |
| C. | \[2\,sin\,\phi \] |
| D. | \[2\,\cos \,\phi \] |
| Answer» B. \[\,\tan \,\phi \] | |
| 5078. |
A long horizontal rod has a bead which can slide along its length, and initially placed at a distance \[L\] from one end \[A\] of the rod. The rod is set in angular motion about \[A\] with constant angular acceleration\[\alpha \]. If the coefficient of friction between the rod and the bead is \[\mu \], and gravity is neglected, then the time after which the bead starts slipping is |
| A. | \[\sqrt{\frac{\mu }{\alpha }}\] |
| B. | \[\frac{\mu }{\sqrt{\alpha }}\] |
| C. | \[\frac{1}{\sqrt{\mu \alpha }}\] |
| D. | Infinitesimal |
| Answer» B. \[\frac{\mu }{\sqrt{\alpha }}\] | |
| 5079. |
A particle describes a horizontal circle in a conical funnel whose inner surface is smooth with speed of 0.5 m/s. What is the height of the plane of circle from vertex of the funnel? |
| A. | 0.25 cm |
| B. | 2 cm |
| C. | 4 cm |
| D. | 2.5 cm |
| Answer» E. | |
| 5080. |
A body of mass \[M\]is kept on a rough horizontal surface (friction coefficient \[\mu \]). A person is trying to pull the body by applying a horizontal force but the body is not moving. The force by the surface on the body is \[F\], where |
| A. | \[F=mg\] |
| B. | \[F=\mu Mgf\] |
| C. | \[Mg\le F\le Mg\sqrt{1+{{\mu }^{2}}}\] |
| D. | \[Mg\,\ge F\,\ge =\mu Mg\sqrt{1+{{\mu }^{2}}}\] |
| Answer» D. \[Mg\,\ge F\,\ge =\mu Mg\sqrt{1+{{\mu }^{2}}}\] | |
| 5081. |
A particle of weight \[W\]rests on a rough inclined plane which makes an angle \[\alpha \] with the horizontal. If the coefficient of static friction \[\mu =2\] tan a, find the horizontal force \[H\] acting transverse to the slope of the plane when the particle is about to slip. |
| A. | \[2W\,\sin \alpha \] |
| B. | \[W\,\sin \,\alpha \] |
| C. | \[\frac{\sqrt{3}}{2}W\,\sin \,\alpha \] |
| D. | \[W\sqrt{3}\,\sin \,\alpha \] |
| Answer» E. | |
| 5082. |
A block of mass 1 kg is at rest on a horizontal table. The coefficient of static friction between the block and the table is 0.5. The magnitude of the force acting upwards at an angle of \[60{}^\circ \] from the horizontal that will just start the block moving is |
| A. | \[5\,N\] |
| B. | \[\frac{20}{2+\sqrt{3}}N\] |
| C. | \[\frac{20}{2-\sqrt{3}}N\] |
| D. | \[10\,N\] |
| Answer» C. \[\frac{20}{2-\sqrt{3}}N\] | |
| 5083. |
The system is pushed by a force \[F\] as shown in figure. All surfaces are smooth except between \[B\] and \[C\]. Friction coefficient between \[B\] and \[C\] is \[\mu \]. Minimum value of \[F\]to prevent block \[B\] from downward slipping is |
| A. | \[\left( \frac{3}{2\mu } \right)mg\] |
| B. | \[\left( \frac{5}{2\mu } \right)mg\] |
| C. | \[\left( \frac{5}{2} \right)\mu mg\] |
| D. | \[\left( \frac{3}{2} \right)\mu mg\] |
| Answer» C. \[\left( \frac{5}{2} \right)\mu mg\] | |
| 5084. |
Given in the figure are two blocks \[A\] and \[B\] of weight 20 N and 100 N, respectively. These are being pressed against a wall by a force \[F\] as shown. If the coefficient of friction between the blocks is 0.1 and between block B and the wall is 0.15, the frictional force applied by the wall on block \[B\] is |
| A. | 100 N |
| B. | 80 N |
| C. | 120 N |
| D. | 150 N |
| Answer» D. 150 N | |
| 5085. |
A block rests on a rough inclined plane making an angle of \[30{}^\circ \] with the horizontal. The coefficient of static friction between the block and the plane is 0.8. If the frictional force on the block is 10 N, the mass of the block (in kg) is \[(take\,g=10\,m/{{s}^{2}})\] |
| A. | 1.6 |
| B. | 4 |
| C. | 2.0 |
| D. | 2.5 |
| Answer» D. 2.5 | |
| 5086. |
A block is placed at the bottom of an inclined plane and projected upwards with some initial speed. It slides up the plane and stops after time \[{{t}_{1}}\]. It begins to slide back down to the bottom in a further time \[{{t}_{2}}\]. The angle of inclination of plane is \[\theta \] and the coefficient of friction between body and the surface is \[\mu \]. Then |
| A. | \[{{t}_{1}}={{t}_{2}}\] |
| B. | \[{{t}_{1}}>{{t}_{2}}\] |
| C. | \[{{t}_{2}}>{{t}_{1}}\] |
| D. | \[{{t}_{1}}=2{{t}_{2}}\] |
| Answer» D. \[{{t}_{1}}=2{{t}_{2}}\] | |
| 5087. |
A tube of length \[L\] is filled completely with an incompressible liquid of mass \[M\]and closed at both the ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity \[\omega \]. The force exerted by the liquid at the other end is |
| A. | \[\frac{ML{{\omega }^{2}}}{2}\] |
| B. | \[ML{{\omega }^{2}}\] |
| C. | \[\frac{ML{{\omega }^{2}}}{4}\] |
| D. | \[\frac{M{{L}^{2}}{{\omega }^{2}}}{2}\] |
| Answer» B. \[ML{{\omega }^{2}}\] | |
| 5088. |
A boy projects a stone vertically perpendicular to the trolley car with a speed \[v\]. If the trolley car moves with \[u\]constant velocity m, the time of flight of the stone is: |
| A. | \[\frac{u+v}{g}\] |
| B. | \[\frac{2v}{g}\] |
| C. | \[\frac{2u}{g}\] |
| D. | none of these |
| Answer» C. \[\frac{2u}{g}\] | |
| 5089. |
Two balls A and B are thrown with speeds \[u\] and u/2, respectively. Both the balls cover the same horizontal distance before returning to the plane of projection. If the angle of projection of ball B is \[15{}^\circ \] with the horizontal, then the angle of projection of A is |
| A. | \[{{\sin }^{-1}}\left( \frac{1}{8} \right)\] |
| B. | \[\frac{1}{2}{{\sin }^{-1}}\left( \frac{1}{8} \right)\] |
| C. | \[\frac{1}{3}{{\sin }^{-1}}\left( \frac{1}{8} \right)\] |
| D. | \[\frac{1}{4}{{\sin }^{-1}}\left( \frac{1}{8} \right)\] |
| Answer» C. \[\frac{1}{3}{{\sin }^{-1}}\left( \frac{1}{8} \right)\] | |
| 5090. |
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 \[\alpha \] is equal to |
| A. | \[30{}^\circ +\,te{{n}^{-1}}(\frac{\sqrt{3}}{2})\] |
| B. | \[45{}^\circ \] |
| C. | \[60{}^\circ \] |
| D. | \[30{}^\circ \,+\,te{{n}^{-1}}(2\sqrt{3})\] |
| Answer» B. \[45{}^\circ \] | |
| 5091. |
Pankaj and Sudhir are playing with two different balls of masses m and \[2m\], respectively. If Pankaj throws his ball vertically up and Sudhir at an angle\[\theta \], both of them stay in our view for the same period. The height attained by the two balls are in the ratio |
| A. | 2 : 1 |
| B. | 0.0423611111111111 |
| C. | \[1:cos\theta \] |
| D. | \[1:sec\theta \] |
| Answer» C. \[1:cos\theta \] | |
| 5092. |
A particle is projected from point \[O\] with velocity \[u\] in a direction making an angle \[\alpha \] with the horizontal. At any instant its position is at point \[p\] at right angles to the initial direction of projection, Its velocity at point \[p\] is |
| A. | \[u\tan \alpha \] |
| B. | \[u\cot \alpha \] |
| C. | \[u\operatorname{cosec}\alpha \] |
| D. | \[u\sec \alpha \] |
| Answer» C. \[u\operatorname{cosec}\alpha \] | |
| 5093. |
A particle is moving on a circular path of radius r with uniform velocity v. The change in velocity when the particle moves from \[P\] to \[Q\] is \[(\angle POQ={{40}^{{}^\circ }})\] |
| A. | \[2v\,\cos \,40{}^\circ \] |
| B. | \[2v\,\sin 40{}^\circ \] |
| C. | \[2v\,\sin \,20{}^\circ \] |
| D. | \[2v\,\cos \,20{}^\circ \] |
| Answer» D. \[2v\,\cos \,20{}^\circ \] | |
| 5094. |
Which of the following statements is false for a particle moving in a circle with a constant angular speed? |
| A. | The acceleration vector points to the centre of the circle. |
| B. | The acceleration vector is tangent to the circle. |
| C. | The velocity vector is tangent to the circle. |
| D. | The velocity and acceleration vectors are perpendiculai to each other. |
| Answer» C. The velocity vector is tangent to the circle. | |
| 5095. |
Two cars of masses \[{{m}_{1\,}}and\,{{m}_{2}}\] are moving in circles of radii \[{{r}_{1\,}}and\,{{r}_{2}}\], respectively. Their speeds are such tha they make complete circles in the same time t. The ratic of their centripetal acceleration is |
| A. | \[{{m}_{1}}\,{{r}_{1}}\,:\,{{m}_{2}}\,{{r}_{2}}\] |
| B. | \[{{m}_{1}}\,:\,{{m}_{2}}\] |
| C. | \[{{r}_{1}}\,:\,{{r}_{2}}\] |
| D. | \[1\,\,:\,\,1\] |
| Answer» D. \[1\,\,:\,\,1\] | |
| 5096. |
An aeroplane is to go along straight line from \[A\] to \[B\], am back again. The relative speed with respect to wind is \[V\] The wind blows perpendicular to line AB with speed v The distance between \[A\] and \[B\] is \[l\]. The total time for round trip is |
| A. | \[\frac{2\ell }{\sqrt{{{V}^{2}}-{{v}^{2}}}}\] |
| B. | \[\frac{2v\ell }{{{V}^{2}}-{{v}^{2}}}\] |
| C. | \[\frac{2V\ell }{{{V}^{2}}-{{v}^{2}}}\] |
| D. | \[\frac{2\ell }{\sqrt{{{V}^{2}}+{{v}^{2}}}}\] |
| Answer» B. \[\frac{2v\ell }{{{V}^{2}}-{{v}^{2}}}\] | |
| 5097. |
A stone is projected from a horizontal plane. It attains maximum height '\[H\]' and strikes a stationary smooth wall and falls on the ground vertically below the maximum height. Assuming the collision to be elastic the height of the point on the wall where ball will strike is |
| A. | \[\frac{H}{2}\] |
| B. | \[\frac{H}{4}\] |
| C. | \[\frac{3H}{4}\] |
| D. | None of these |
| Answer» D. None of these | |
| 5098. |
A person walks at the rate of \[3\,km/hr\]. Rain appears to him in vertical direction at the rate of \[3\sqrt{3}km/hr\]. Find the magnitude and direction of true velocity of rain. |
| A. | \[6\,km/hr\], inclined at an angle of \[45{}^\circ \] to the vertical towards the person's motion. |
| B. | \[3\,km/hr\], inclined at an angle of \[30{}^\circ \] to the vertical towards the person's motion. |
| C. | \[6\,km/hr\], inclined at an angle of \[30{}^\circ \] to the vertical towards the person's motion. |
| D. | \[6\,km/hr\], inclined at an angle of \[60{}^\circ \] to the vertical towards the person's motion. |
| Answer» D. \[6\,km/hr\], inclined at an angle of \[60{}^\circ \] to the vertical towards the person's motion. | |
| 5099. |
A particle is moving along a circular path. The angular velocity, linear velocity, angular acceleration, and centripetal acceleration of the particle at any instant, respectively, are \[\vec{w},\,\vec{v},\,\vec{\alpha }\,and\,{{\vec{a}}_{c}}\]. Which of the following relations is not correct? |
| A. | \[\vec{w}\bot \vec{v}\] |
| B. | \[\vec{w}\bot \vec{\alpha }\] |
| C. | \[\vec{w}\bot {{\vec{\alpha }}_{c}}\] |
| D. | \[\vec{v}\bot {{\vec{\alpha }}_{c}}\] |
| Answer» C. \[\vec{w}\bot {{\vec{\alpha }}_{c}}\] | |
| 5100. |
A bird is flying towards north with a velocity \[40km\,{{h}^{-1}}\]and a train is moving with velocity \[40km\,{{h}^{-1}}\] towards east. What is the velocity of the bird noted by a man in the train? |
| A. | \[40\sqrt{2}\,km\,{{h}^{-1}}\,N-E\] |
| B. | \[40\sqrt{2}\,km\,{{h}^{-1}}\,S-E\] |
| C. | \[40\sqrt{2}\,km\,{{h}^{-1}}\,N-W\] |
| D. | \[40\sqrt{2}\,km\,{{h}^{-1}}\,S-W\] |
| Answer» D. \[40\sqrt{2}\,km\,{{h}^{-1}}\,S-W\] | |