Question 2 : A mass <em>A</em> is released from the top of a frictionless inclined plane 18 m long and reaches the bottom 3 second later. At the instant when <em>A</em> is released, a second mass <em>B</em> is projected upwards along the plane from the bottom with a certain initial velocity. The mass <em>B</em> travels a distance up the plane, stops and returns to the bottom simultaneously with A. The two masses do not collide. Initial velocity of <em>B</em> is<img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c21c4bec8070e4e15066"/>
Question 4 : Two blocks of masses 2 kg and 5 kg are at rest on ground. The masses are connected by a string passing over a frictionless pulley which is under the influence of a constant upward force F = 50 N. The accelerations of 5 kg and 2 kg masses are <br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75ec52b5f89758f2d4f46d' height='120' width='80' >
Question 5 : A 3 kg ball strikes a heavy rigid wall with a speed of 10 m/s at an angle of 60<font face="Symbol">°</font> with the wall. It gets reflected with the same speed at 60<font face="Symbol">°</font> with the wall. If the ball is in contact with the wall for 0.2 s, the average force exerted on the ball by the wall is <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c1cdbfef6349df00fdf7"/>
Question 6 : The coefficient of friction between two surfaces is μ = 0.8. The tension in the string shown in the figure is - <br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75f13b491ec9580069869d' height='99' width='126' >
Question 7 :
A bob of mass 3.9 kg is suspended from a string of length 50 cm and is at rest. Another body of mass 100 gm, which is moving horizontally with a velocity of 160 m/s strikes the bob and sticks to it. The incorrect statement is, (Take <em>g</em> = 10 m/s<sup>2</sup>)
Question 8 :
A light string passing over a smooth light pulley connects two blocks of masses {tex} m _ { 1 } {/tex} and {tex} m _ { 2 } {/tex} (vertically). If the acceleration of the system is {tex} g / 8 , {/tex} then the ratio of the masses is
Question 9 :
A body subjected to three concurrent forces is found to be in equilibrium. The resultant of any two forces :
Question 10 : Two masses {tex} A {/tex} and {tex} B {/tex} of {tex}10 kg{/tex} and {tex}5 kg{/tex} respectively are connected with a string passing over a frictionless pulley fixed at the corner of a table as shown. The coefficient of static friction of A with table is {tex}0.2{/tex}. The minimum mass of {tex} C {/tex} that may be placed on A to prevent it from moving is<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5da998413ff4ff5cad668a23"><br>
Question 11 :
A machine gun has a mass 5 kg. It fires 50 gram bullets at the rate of 30 bullets per minute at a speed of 400 ms<sup>-1</sup>. What force is required to keep the gun in position ?
Question 12 :
{tex}\mathbf {Assertion}{/tex} :Pulling a lawn roller is easier than pushing it.<br> {tex}\mathbf {Reasoning}{/tex} : Pushing increases the apparent weight and hence the force of friction.
Question 13 : For the system shown in figure, the pulleys are light and frictionless. The tension in the string will be -<br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75eda4491ec9580069854e' height='72' width='137' >
Question 15 :
If {tex} \mu _ { s } , \mu _ { k } {/tex} and {tex} \mu _ { r } {/tex} are coefficients of static friction, sliding friction and rolling friction, then<br>
Question 16 : A pearl of mass m is in a position to slide over a smooth wire. At the initial instant the pearl is in the middle of the wire. The wire moves linearly in a horizontal plane with an acceleration a in a direction having angle θ with the wire. The acceleration of the pearl with reference to wire is <br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75eebb4389b1556ddf0778' height='100' width='145' >
Question 17 :
{tex} \mathrm { Assertion }: {/tex} Force is required to move a body uniformly along a circle.<br>{tex} \mathrm { Reason }: {/tex} When the motion is uniform, acceleration is zero.
Question 18 :
A {tex} 20 \mathrm { kg } {/tex} block is initially at rest on a rough horizontal surface. A horizontal force of {tex} 75 \mathrm { N } {/tex} is required to set the block in motion. After it is in motion, a horizontal force of {tex} 60 \mathrm { N } {/tex} is required to keep the block moving with constant<br>speed. The coefficient of static friction is<br>
Question 19 :
A heavy uniform chain lies on a horizontal table-top. If the coefficient of friction between the chain and table surface is {tex} 0.25 , {/tex} then the maximum fraction of length of the chain,<br>that can hang over one edge of the table is<br>
Question 20 :
Two bodies of mass 1 kg and 2 kg move towards each other in mutually perpendicular direction with the velocities 3 m/s and 2 m/s respectively. If the bodies stick together after collision the heat liberated will be
Question 21 :
When forces {tex} F _ { 1 } , F _ { 2 } , F _ { 3 } {/tex} are acting on a particle of mass {tex} m {/tex} such that {tex} F _ { 2 } {/tex} and {tex} F _ { 3 } {/tex} are mutually perpendicular, then the particle remains stationary. If the force {tex} F _ { 1 } {/tex} is now removed then the acceleration of the particle is
Question 22 :
A force of− <em>F</em><em>k̂</em> acts on <em>O</em>, the origin of the coordinate system. The torque about the point<br/> (1, −1) is
Question 23 :
{tex} \mathrm { Assertion }:{/tex} The acceleration produced by a force in the motion of a body depends only upon its mass.<br>{tex} \mathrm { Reason }:{/tex} Larger is the mass of the body, lesser will be the acceleration produced.
Question 24 :
A marble block of mass 2 kg lying on ice when given a velocity of 6 m/s is stopped by friction in 10 s. Then the coefficient of friction is
Question 25 :
A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?
Question 26 :
The motion of a rocket is based on the principle of conservation of
Question 27 :
Two forces are such that the sum of their magnitudes is {tex} \mathrm { 18 N } {/tex} and their resultant is {tex} \mathrm {12 N } {/tex} which is perpendicular to the smaller force. Then the magnitudes of the forces are
Question 28 :
A lift is moving downwards with an acceleration equal to acceleration due to gravity. A body of mass {tex} M {/tex} kept on the floor of the lift is pulled horizontally. If the coefficient of friction is {tex} \mu , {/tex} then the frictional resistance offered by the body is
Question 29 : A block <em>m</em><sub>1</sub> of mass 2.0 kg is moving on a frictionless horizontal surface with a velocity of 1.0 m/s towards another block <em>m</em><sub>2</sub> of equal mass kept at rest as shown. The spring constant of the spring fixed at one end of <em>m</em><sub>2</sub> is 100 N/m. The maximum compression of the spring is<img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c2224bec8070e4e1506d"/>
Question 30 :
A force of 10 Newton acts on a body of mass {tex} 20 \mathrm { kg } {/tex} for 10 seconds.<br>Change in its momentum is<br>
Question 31 :
The minimum velocity (in ms<sup>-1</sup>) with which a car driver must traverse a flat curve of radius 150 m and coefficient of friction 0.6 to avoid skidding is-
Question 32 :
Two bodies of masses 2 kg and 4 kg are moving with velocities 10 m/s and 2 m/s towards each other. The velocity of their centre of mass is
Question 33 : A block is kept on a frictionless inclined surface with angle of inclination {tex} ^ { \prime } \alpha {/tex}. The incline is given an acceleration ' {tex} 'a' {/tex} to keep the block stationary. Then {tex} a {/tex} is equal to
<img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5dc28cc44548337453d20df3">
Question 34 :
A car having a mass of {tex} 1000 \mathrm { kg } {/tex} is moving at a speed of {tex} \mathrm 30 {/tex} metres/sec. Brakes are applied to bring the car to rest. If the frictional force between the tyres and the road<br>surface is 5000 newtons, the car will come to rest in<br>
Question 35 :
A {tex} 500 {/tex} kg horse pulls a cart of mass {tex}1500{/tex} kg along a level road with an acceleration of {tex} 1 \,\mathrm { ms } ^ { - 2 } . {/tex} If the coefficient of sliding friction is {tex} 0.2 , {/tex} then the force exerted by the horse<br>in forward direction is<br>
Question 36 :
A body of mass {tex} 2 \mathrm { kg } {/tex} is kept by pressing to a vertical wall by a force of {tex} 100 { N } {/tex}. The coefficient of friction between wall and body is {tex} 0.3 . {/tex} Then the frictional force is equal to
Question 37 :
A body of mass {tex} 10 \mathrm { kg } {/tex} is lying on a rough plane inclined at an angle of {tex} 30 ^ { \circ } {/tex} to the horizontal and the coefficient of friction is {tex} 0.5 . {/tex} the minimum force required to pull the<br>body up the plane is<br>
Question 38 :
A 60 kg man stands on a spring scale in a lift. At some instant he finds that the scale reading has changed from 60 kg to 50 kg for a while and then comes back to the original mark . What should he conclude?
Question 39 :
A body of mass 2 kg moves vertically downwards with an acceleration <em>a</em> = 19.6 m/s<sup>2</sup>. The force acting on the body simultaneously with the force of gravity is (<em>g</em> = 9.8 m/s<sup>2</sup>, neglect air resistance)
Question 40 :
In which of the following cases forces may not be required to keep the<br>
Question 41 : A body of mass {tex} m {/tex} rests on horizontal surface. The coefficient of friction between the body and the surface is {tex} \mu {/tex}. If the mass is pulled by a force {tex} P {/tex} as shown in the figure, the limiting friction between body and surface will be<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5dbd5f26ec8cf4127b930812"><br>
Question 42 :
A body of mass 1.5 kg is thrown vertically upwards with an initial velocity of 40 m/s reaches its highest point after 3 s. The air resistance acting on the body during the ascent is (assuming air resistance to be uniform, <em>g</em> = 10 m/s<sup>2</sup>)
Question 43 :
A fireman of mass 60kg slides down a pole. He is pressing the pole with a force of 600 N. The coefficient of friction between the hands and the pole is 0.5, with what acceleration will the fireman slide down (g = 10 m/s<sup>2</sup>)
Question 44 : Three blocks <em>m</em><sub>1</sub>, <em>m</em><sub>2</sub> and <em>m</em><sub>3</sub> of masses 8 kg, 3 kg and<br/> 1 kg are placed in contact on a smooth surface. Forces<br/> <em>F</em><sub>1</sub> = 140 N and <em>F</em><sub>2</sub> = 20 N are acting on blocks <em>m</em><sub>1</sub> and <em>m</em><sub>3</sub> respectively as shown. The reaction between blocks <em>m</em><sub>2</sub> and <em>m</em><sub>3</sub> is<img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c07df1a5a149feab996a"/>
Question 45 :
The resultant of two forces, one double the other in magnitude, is perpendicular to the smaller of the two forces. The angle between the two forces is
Question 46 : Two point masses connected by an ideal string are placed on a smooth horizontal surface as shown in the diagram. A sharp impulse of 10 kg-m/s is given to the 5 kg mass. The velocity of the 10 kg mass will be<img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c20ff1a5a149feab9a15"/>
Question 47 : A rough vertical board has an acceleration <em>a</em> so that a 2kg block pressing against it does not fall. The coefficient of friction between the block and the board is <font face="Symbol">µ</font> then<img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c0c8bfef6349df00fda7"/>
Question 48 :
{tex} A {/tex} body {tex} B {/tex} lies on a smooth horizontal table and another body {tex} A {/tex} is placed on {tex} B {/tex}. The coefficient of friction between<br>{tex} A \,\text{and} \, B {/tex} is {tex} \mu {/tex}. What acceleration given to B will cause slipping to occur between {tex} A {/tex} and {tex} B {/tex}<br>
Question 49 :
A parachutist of weight {tex} 'w' {/tex} strikes the ground with his legs fixed and comes to rest with an upward acceleration of magnitude {tex}3 \ g {/tex}. Force exerted on him by ground during landing is
Question 50 : A two-car train, with data as given in figure is pulled by a child on a horizontal frictionless surface. The strings are massless. The force exerted by car A on the string S is <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c096bfef6349df00fd87"/>
