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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.
| 2251. |
A small mass slides down a fixed inclined plane of inclination 6 with the horizontal. The coefficient of friction is \[\mu \text{ }=\text{ }{{\mu }_{0}}x\]Where \[x\] is the distance through which the mass slides down and \[{{\mu }_{0}}\] is a constant? Then he speed is maximum after the mass covers a distance of |
| A. | \[\frac{\cos \theta }{{{\mu }_{0}}}\] |
| B. | \[\frac{\sin \theta }{{{\mu }_{0}}}\] |
| C. | \[\frac{tan\theta }{{{\mu }_{0}}}\] |
| D. | \[\frac{2tan\theta }{{{\mu }_{0}}}\] |
| Answer» D. \[\frac{2tan\theta }{{{\mu }_{0}}}\] | |
| 2252. |
A block B is pushed momentarily along a horizontal surface with an initial velocity V. If p is the coefficient of sliding friction between Band the surface, block B will come to rest after a time |
| A. | \[\frac{g\mu }{V}\] |
| B. | \[\frac{g}{V}\] |
| C. | \[\frac{V}{g}\] |
| D. | \[\frac{V}{g\left( \mu \right)}\] |
| Answer» E. | |
| 2253. |
A horizontal force of 10 N is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is 0.2. The weight of the block is |
| A. | 20 N |
| B. | 50 N |
| C. | 100 N |
| D. | 2 N |
| Answer» E. | |
| 2254. |
The acceleration of the system shown in the figure is given by the expression (coefficient of friction between m, and surface is \[\mu \]) |
| A. | \[a=\frac{\left( {{m}_{2}}-\mu {{m}_{1}} \right)}{\left( {{m}_{1}}+{{m}_{2}} \right)}\] |
| B. | \[a=\frac{{{m}_{1}}g}{\left( {{m}_{1}}+{{m}_{2}} \right)}\] |
| C. | \[a=\frac{\left( {{m}_{1}}+\mu {{m}_{2}} \right)}{\left( {{m}_{1}}+{{m}_{2}} \right)g}\] |
| D. | \[a=\frac{\left( {{m}_{1}}-{{m}_{2}} \right)\mu }{\left( {{m}_{1}}+{{m}_{2}} \right)g}\] |
| Answer» B. \[a=\frac{{{m}_{1}}g}{\left( {{m}_{1}}+{{m}_{2}} \right)}\] | |
| 2255. |
It is difficult to move a cycle with brakes on because |
| A. | rolling friction opposes motion on road |
| B. | sliding friction opposes motion on road |
| C. | rolling friction is more than sliding friction |
| D. | sliding friction is more than rolling friction |
| Answer» E. | |
| 2256. |
The upper half of an inclined plane of inclination \[\theta \]is perfectly smooth while lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom, if the coefficient of friction between the block and lower half of the plane is given by |
| A. | \[\mu =\frac{2}{\tan \theta }\] |
| B. | \[\mu =2\tan \theta \] |
| C. | \[\mu =2\tan \theta \] |
| D. | \[\mu =\frac{1}{\tan \theta }\] |
| Answer» C. \[\mu =2\tan \theta \] | |
| 2257. |
In the diagram shown, friction is completely absent. If a force F has been applied on the wedge such that it moves with a constant velocity than value of normal reaction N' is |
| A. | \[>F\] |
| B. | \[<F\] |
| C. | \[=F\] |
| D. | cannot find |
| Answer» B. \[<F\] | |
| 2258. |
A 20 kg block B is suspended from a cord attached to a 40 kg cart A. Find the ratio of the acceleration of block in cases (i) and (ii) shown in the figure immediately after the system is released from rest. (neglect friction) |
| A. | \[\frac{\sqrt{2}}{3}\] |
| B. | \[3\sqrt{2}\] |
| C. | \[\frac{3}{2}\] |
| D. | \[\frac{3}{2\sqrt{2}}\] |
| Answer» E. | |
| 2259. |
A uniform rod AB of length 3r remains in equilibrium on a hemispherical bowl of radius r as shown in figure. Ignoring friction, the inclination of the rod \[\theta \]with the horizontal is |
| A. | \[{{\cos }^{-1}}\left( 1/3 \right)\] |
| B. | \[{{\sin }^{-1}}\left( 1/3 \right)\] |
| C. | \[{{\cos }^{-1}}\left( 0.9 \right)\] |
| D. | \[{{\sin }^{-1}}\left( 0.9 \right)\] |
| Answer» D. \[{{\sin }^{-1}}\left( 0.9 \right)\] | |
| 2260. |
A conveyor belt is moving at a constant speed of 2m/s. A box is gently dropped on it. The coefficient of friction between them is\[\mu =0.5\]. The distance that the box will move relative to belt before coming to rest on it taking \[g=10m{{s}^{-2}}\], is |
| A. | 1.2 m |
| B. | 0.6 m |
| C. | zero |
| D. | 0.4 m |
| Answer» E. | |
| 2261. |
A balloon with mass 'm' is descending down with an acceleration 'a' (where a < g). How much mass should be removed from it so that it starts moving up with an acceleration 'a'? |
| A. | \[\frac{2ma}{g+a}\] |
| B. | \[\frac{2ma}{g-a}\] |
| C. | \[\frac{ma}{g+a}\] |
| D. | \[\frac{ma}{g-a}\] |
| Answer» B. \[\frac{2ma}{g-a}\] | |
| 2262. |
A system shown in the figure. Assume that cylinder remains in contact with the sedge and block hence the velocity of cylinder is |
| A. | \[\frac{\sqrt{19-4\sqrt{3}}}{2}\text{ m/s}\] |
| B. | \[\frac{\sqrt{13}}{2}\text{ m/s}\] |
| C. | \[\sqrt{3}\text{m/s}\] |
| D. | \[\sqrt{7}\text{ m/s}\] |
| Answer» E. | |
| 2263. |
A string of negligible mass going over a clamped pulley of mass m supports a block of mass Mas shown in the figure. The force on the pulley by the clamp is given by |
| A. | \[\sqrt{2}\text{ Mg}\] |
| B. | \[\sqrt{2}\text{ mg}\] |
| C. | \[\sqrt{{{\left( M+m \right)}^{2}}+{{m}^{2}}}\text{ g}\] |
| D. | \[\sqrt{{{\left( M+m \right)}^{2}}+{{M}^{2}}}\text{ g}\] |
| Answer» E. | |
| 2264. |
Two smooth cylindrical bars weighing W each lie next to each other in contact. A similar third bar is placed over the two bars as shown in figure. Neglecting friction, the minimum horizontal force on each lower bar necessary to keep them together is |
| A. | \[\frac{W}{2}\] |
| B. | \[W\] |
| C. | \[\frac{W}{\sqrt{3}}\] |
| D. | \[\frac{W}{2\sqrt{3}}\] |
| Answer» E. | |
| 2265. |
A ball of mass 0.2 kg is thrown vertically upwards by applying a force by hand. If the hand moves 0.2 m while applying the force and the ball goes up to 2 m height further, find the magnitude of the force. (Consider\[\,g\text{ }=\text{ }10\text{ }m/{{s}^{2}}\]). |
| A. | 4 N |
| B. | 16 N |
| C. | 20 N |
| D. | 22 N |
| Answer» E. | |
| 2266. |
Two blocks of masses m and M are connected by means of a metal wire of cross-sectional area a passing over a frictionless fixed pulley as shown in the figure. The system is then released. If \[M=2\], then the tension per unit crossectional area produced in the wire is |
| A. | \[\frac{2mg}{3A}\] |
| B. | \[\frac{4mg}{3A}\] |
| C. | \[\frac{mg}{A}\] |
| D. | \[\frac{3mg}{4A}\] |
| Answer» C. \[\frac{mg}{A}\] | |
| 2267. |
Two blocks of mass \[{{M}_{1}}=\text{ }20\text{ }kg\]and \[{{M}_{2}}=\text{ }12\text{ }kg\]are connected by a metal rod of mass 8 kg. The system is pulled vertically up by applying a force of 480 N as shown. The tension at the mid-point of the rod is: |
| A. | 144 N |
| B. | 96 N |
| C. | 240 N |
| D. | 192 N |
| Answer» E. | |
| 2268. |
In the figure acceleration of bodies A, B and C are shown with directions. Values b and c are w.r.t. ground whereas a is acceleration of block A w.r.t. sedge C. Acceleration of block A w.r.t. ground is |
| A. | \[\sqrt{{{\left( b+c \right)}^{2}}+{{a}^{2}}}\] |
| B. | \[c-\left( a+b \right)\cos \theta \] |
| C. | \[\sqrt{{{\left( b+c \right)}^{2}}+{{c}^{2}}-2\left( b+c \right).c.\cos \theta }\] |
| D. | \[\sqrt{{{\left( b+c \right)}^{2}}+{{c}^{2}}+2\left( b+c \right).c.\cos \theta }\] |
| Answer» D. \[\sqrt{{{\left( b+c \right)}^{2}}+{{c}^{2}}+2\left( b+c \right).c.\cos \theta }\] | |
| 2269. |
Three blocks A, B and C of masses 4 kg, 2 kg and 1 kg respectively, are in contact on a motionless surface, as shown. If a force of 14 N is applied on the 4 kg block then the contact force between A |
| A. | 6 N |
| B. | 8 N |
| C. | 18 N |
| D. | 2 N |
| Answer» B. 8 N | |
| 2270. |
A smooth ring P of mass m can slide on a fixed horizontal rod. A string tied to the ring passes over a fixed pulley and carries a block Q of mass (mil) as shown in the figure. At an instant, the string between the ring and the pulley makes an angle \[60{}^\circ \]with the rod. The initial acceleration of the ring is |
| A. | \[\frac{2g}{3}\] |
| B. | \[\frac{2g}{6}\] |
| C. | \[\frac{2g}{9}\] |
| D. | \[\frac{g}{3}\] |
| Answer» D. \[\frac{g}{3}\] | |
| 2271. |
. One end of a massless rope, which passes over a massless and frictionless pulley P is tied to a hook C while the other end is free. Maximum tension that the rope can bear is 360 N. With what value of maximum safe acceleration (in\[m{{s}^{-2}}\]) can a man of 60 kg climb on the rope? |
| A. | 16 |
| B. | 6 |
| C. | 4 |
| D. | 8 |
| Answer» D. 8 | |
| 2272. |
A horizontal uniform rope of length L, resting on a frictionless horizontal surface, is pulled at one end by force F. What is the tension in the rope in a distance l from the end where the force is applied? |
| A. | (a)\[F\left( 1-\frac{l}{L} \right)\] |
| B. | \[2F\left( 1-\frac{l}{2L} \right)\] |
| C. | \[\frac{F}{L}\] |
| D. | \[\frac{F}{l}\left( 1-\frac{l}{L} \right)\] |
| Answer» B. \[2F\left( 1-\frac{l}{2L} \right)\] | |
| 2273. |
A pail filled with sand has a total mass of 60 kg. A crane is lowering it such that it has an initial downward acceleration of\[1.5\text{ }m/{{s}^{2}}\]. A hole in the pail allows sand to leak out. If the force exerted by the crane on the pail does not change, what mass of sand must leak out before the downward acceleration decreases to zero? |
| A. | 9.2 kg |
| B. | 20 kg |
| C. | 40 kg |
| D. | 51 kg |
| Answer» B. 20 kg | |
| 2274. |
A weight W is supported by two cables as shown. The tension in the cable making angle \[\theta \] with horizontal will be the minimum when the value of \[\theta \] is. |
| A. | 0 |
| B. | \[30{}^\circ \] |
| C. | \[60{}^\circ \] |
| D. | \[45{}^\circ \] |
| Answer» C. \[60{}^\circ \] | |
| 2275. |
A body of mass 5 kg under the action of constant force \[\vec{F}={{F}_{x}}\hat{i}+{{F}_{y}}\hat{j}\] has velocity at \[t=0\text{ }s\] as \[\vec{v}=(6\hat{i}-2\hat{j})m/s\]and at \[t=\text{1}0\text{ }s\]gas\[\vec{v}=6\hat{j}\text{ m/s}\]. The force F is: |
| A. | \[\left( -3\hat{i}+4\hat{j} \right)\text{ N}\] |
| B. | \[\left( -\frac{3}{5}\hat{i}+\frac{4}{5}\hat{j} \right)\text{ N}\] |
| C. | \[\left( 3\hat{i}-4\hat{j} \right)\text{ N}\] |
| D. | \[\left( \frac{3}{5}\hat{i}-\frac{4}{5}\hat{j} \right)\text{ N}\] |
| Answer» B. \[\left( -\frac{3}{5}\hat{i}+\frac{4}{5}\hat{j} \right)\text{ N}\] | |
| 2276. |
In the figure (i) an extensible string is fixed at one end and the other end is pulled by a tension T. In figure (ii) another identical string is pulled by tension T at both the ends. The ratio of elongation in equilibrium of string in (i) to the elongation of string in (ii) is |
| A. | \[1:1\] |
| B. | \[1:2\] |
| C. | \[2:1\] |
| D. | (d)\[0\] |
| Answer» B. \[1:2\] | |
| 2277. |
Two monkeys of masses 10 kg and 8 kg are moving along a vertical rope which is light and inextensible, the former climbing up with an acceleration of \[2m/{{s}^{2}}\] while the latter coming down with a uniform velocity of \[2m/s\]. Find the tension (in newtons). |
| A. | 200 N |
| B. | 150 N |
| C. | 300 N |
| D. | 100 N |
| Answer» B. 150 N | |
| 2278. |
Two blocks \[{{m}_{1}}=5gm\] and\[{{m}_{2}}=\text{10}gm\] are hung vertically over a light frictionless pulley as shown here. What is the acceleration of the masses when they are left free? (Where g is acceleration due to gravity) |
| A. | \[g/3\] |
| B. | \[g/2\] |
| C. | \[g\] |
| D. | \[g/5\] |
| Answer» B. \[g/2\] | |
| 2279. |
One end of string of length l is connected to a particle of mass 'm' and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed V the net force on the particle (directed towards center) will be (T represents the tension in the string) |
| A. | \[T+\frac{m{{v}^{2}}}{l}\] |
| B. | \[T-\frac{m{{v}^{2}}}{l}\] |
| C. | Zero |
| D. | T |
| Answer» E. | |
| 2280. |
A triangular block of mass M with angles\[30{}^\circ \],\[~60{}^\circ \], and \[90{}^\circ \] rests with its \[30{}^\circ -90{}^\circ \]side on a horizontal table. A cubical block of mass m rests on the \[60{}^\circ -30{}^\circ \] side. The acceleration which M must have relative to the table to keep m stationary relative to the triangular block assuming frictionless contact is |
| A. | \[g\] |
| B. | \[\frac{g}{\sqrt{2}}\] |
| C. | (c)\[\frac{g}{\sqrt{3}}\] |
| D. | \[\frac{g}{\sqrt{5}}\] |
| Answer» D. \[\frac{g}{\sqrt{5}}\] | |
| 2281. |
An overweight acrobat, "weighing" in at 115 kg, wants to perform a single hand stand. He tries to cheat by resting one foot against a smooth frictionless vertical wall. The horizontal force there is 130 N. What is the magnitude of the force exerted by the floor on his hand? Answer in N. |
| A. | 1134 |
| B. | 1257 |
| C. | 997 |
| D. | 1119 |
| Answer» B. 1257 | |
| 2282. |
A block A of mass 7 kg is placed on a frictionless table. A thread tied to it passes over a frictionless pulley and carries a body B of mass 3 kg at the other end. The acceleration of the system is (given \[g=10m{{s}^{-2}}\]) |
| A. | \[100m/{{s}^{-2}}\] |
| B. | \[3m/{{s}^{-2}}\] |
| C. | \[10m/{{s}^{-2}}\] |
| D. | \[30m/{{s}^{-2}}\] |
| Answer» C. \[10m/{{s}^{-2}}\] | |
| 2283. |
Two blocks of masses 2 kg and 4 kg are attached by an inextensible light string as shown in the figure. If a force of 120 N pulls the blocks vertically upward, the tension in the string is (Take\[g\text{ }=\text{ }10\text{ }m{{s}^{-2}}\]) |
| A. | 20N |
| B. | 15N |
| C. | 35N |
| D. | 40N |
| Answer» E. | |
| 2284. |
The elevator shown in fig. is descending with an acceleration of\[2\text{ }m/{{s}^{2}}\]. The mass of the block \[A=0.5\text{ }kg.\] The force exerted by the block A on block B is |
| A. | 2N |
| B. | 4N |
| C. | 6N |
| D. | 8N |
| Answer» C. 6N | |
| 2285. |
A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads 49 N, when the lift is stationary. If the lift moves downward with an acceleration of \[5\text{ }m/{{s}^{2}}\], the reading of the spring balance will be |
| A. | 24N |
| B. | 74N |
| C. | 15N |
| D. | 49N |
| Answer» B. 74N | |
| 2286. |
Which of the following is true about acceleration, for the system? |
| A. | Acceleration is more in A, when force is applied on A. |
| B. | Acceleration is more in B, when force is applied on B. |
| C. | Acceleration is same and does not depend on whether the force is applied on \[\,{{m}_{1}}\] or \[\,{{m}_{2}}\] |
| D. | Acceleration depends on the tension in the tiring. |
| Answer» D. Acceleration depends on the tension in the tiring. | |
| 2287. |
For the system shown in figure, the correct expression is |
| A. | \[{{F}_{3}}={{F}_{1}}+F{{ }_{2}}\] |
| B. | \[{{F}_{3}}=\frac{{{m}_{3}}F}{{{F}_{1}}+F{{ }_{2}}+{{F}_{3}}}\] |
| C. | \[{{F}_{3}}=\frac{{{m}_{3}}F}{{{m}_{1}}+{{m}_{2}}+{{m}_{3}}}\] |
| D. | \[\,{{F}_{3}}=\frac{{{m}_{3}}F}{{{m}_{1}}+{{m}_{2}}}\] |
| Answer» D. \[\,{{F}_{3}}=\frac{{{m}_{3}}F}{{{m}_{1}}+{{m}_{2}}}\] | |
| 2288. |
Three identical blocks of masses \[m=2\text{ }kg\]are drawn by a force \[F=\text{ }10.2\text{ }N\] with an acceleration of \[0.6\text{ }m{{s}^{-2}}\] on a frictionless surface, then what is the tension (in N) in the string between the blocks B and C? |
| A. | 92 |
| B. | 3.4 |
| C. | 4 |
| D. | 9.8 |
| Answer» C. 4 | |
| 2289. |
A solid sphere of 2 kg is suspended from a horizontal beam by two supporting wires as shown in fig. Tension in each wire is approximately \[\left( g=\text{ }10m{{s}^{-2}} \right)\] |
| A. | 30 N |
| B. | 20 N |
| C. | 10 N |
| D. | 5 N |
| Answer» C. 10 N | |
| 2290. |
Two blocks A and B of masses 3 m and m respectively are connected by a massless and inextensible string. The whole system is suspended by massless spring as shown in figure. The magnitudes of acceleration of A and B immediately after the string is cut, are respectively: |
| A. | \[\frac{g}{3},g\] |
| B. | \[~g,\text{ }g\] |
| C. | \[\frac{g}{3},\frac{g}{3}\] |
| D. | \[g,\frac{g}{3}\] |
| Answer» B. \[~g,\text{ }g\] | |
| 2291. |
If two masses (M & m) are connected on a horizontal plane and a force is applied on the combination, then the tension T depends on the |
| A. | force applied on the system |
| B. | whether force is applied on M or m |
| C. | both [a] and [b] |
| D. | Can't be predicted. |
| Answer» C. both [a] and [b] | |
| 2292. |
The force 'F' acting on a particle of mass 'm' is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from zero to 8 s is: |
| A. | 24 Ns |
| B. | 20 Ns |
| C. | 12 Ns |
| D. | 6 Ns |
| Answer» D. 6 Ns | |
| 2293. |
A person of mass 60 kg is inside a lift of mass 940 kg and presses the button on control panel. The lift starts moving upwards with an acceleration\[1.0\text{ }m/{{s}^{2}}\]. If \[g=\text{ }10\text{ }m{{s}^{-2}}\], the tension in the supporting cable is |
| A. | 8600 N |
| B. | 9680 N |
| C. | 11000 N |
| D. | 1200 N |
| Answer» D. 1200 N | |
| 2294. |
For the given situation as shown in the figure, the value of \[\theta \] to keep the system in equilibrium will be |
| A. | \[30{}^\circ \] |
| B. | \[45{}^\circ \] |
| C. | \[0{}^\circ \] |
| D. | \[90{}^\circ \] |
| Answer» C. \[0{}^\circ \] | |
| 2295. |
If the coefficient of friction between all surfaces is 0.5, then find the minimum force F to have equilibrium of system. (assume strings and pulleys are massless) |
| A. | \[\frac{4000}{17}N\] |
| B. | \[\frac{1000}{17}N\,\] |
| C. | \[\frac{2000}{17}N\,\] |
| D. | \[\frac{500}{17}N\,\] |
| Answer» D. \[\frac{500}{17}N\,\] | |
| 2296. |
A particle of mass m is made to move with uniform speed v along the perimeter of a regular polygon of n sides, inscribed in a circle of radius a. The magnitude of impulse applied at each comer of the polygon is : |
| A. | \[2mv\sin \frac{\pi }{n}\] |
| B. | \[mv\sin \frac{\pi }{n}\] |
| C. | \[mv\sin \frac{n}{\pi }\] |
| D. | \[mv\sin \frac{n}{\pi }\] |
| Answer» B. \[mv\sin \frac{\pi }{n}\] | |
| 2297. |
In the figure shown, the pulleys and strings are massless. The acceleration of the block of mass 4 m just after the system is released from rest is \[(\theta ={{\sin }^{-1}}3/5)\] |
| A. | \[\frac{2g}{5}\]downwards |
| B. | \[\frac{2g}{5}\] upwards |
| C. | \[\frac{5g}{11}\]downwards |
| D. | \[\frac{5g}{11}\]upwards |
| Answer» D. \[\frac{5g}{11}\]upwards | |
| 2298. |
A 5000 kg rocket is set for vertical firing. The exhaust speed is\[800m{{s}^{-1}}\]. To give an initial upward acceleration of\[20m{{s}^{-2}}\], the amount of gas ejected per second to supply the needed thrust will be \[\left( g=10m{{s}^{-2}} \right)\] |
| A. | \[127.5\text{ }kg\text{ }{{s}^{-1}}\] |
| B. | \[187.5\text{ }kg\text{ }{{s}^{-1}}\] |
| C. | \[185.5\text{ }kg\text{ }{{s}^{-1}}\] |
| D. | \[137.5\text{ }kg\text{ }{{s}^{-1}}\] |
| Answer» C. \[185.5\text{ }kg\text{ }{{s}^{-1}}\] | |
| 2299. |
. A bullet is fired from a gun. The force on the bullet is given by \[F=600-2\times {{10}^{5}}t\]where. F is in newton and t in second. The force on the bullet becomes zero as soon as it leaves the barrel. What is the average impulse imparted to the bullet? |
| A. | 1.8 N-s |
| B. | zero |
| C. | 9 N-s |
| D. | 0.9 N-s |
| Answer» E. | |
| 2300. |
If a cricketer catches a ball of mass \[150\text{ }gm\]moving with a velocity of\[20\text{ }m/s\], then he experiences a force of (Time taken to complete the catch is sec.) |
| A. | 300 N |
| B. | 30 N |
| C. | 3 N |
| D. | 0.3 N |
| Answer» C. 3 N | |