Laws of Motion & Friction · JEE Main previous year questions

A block of mass $5\text{ kg}$ is placed at rest on a table of rough surface. Now, if a force of $30\text{ N}$ is applied in the direction parallel to surface of the table, the block slides through a distance of $50\text{ m}$ in an interval of time $10\text{ s}$. Coefficient of kinetic friction is (given, $g=10{\text{ ms}}^{-2}$):

1. A.0.25
2. B.0.75
3. C.0.60
4. D.0.50

Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the following {Assume negligible air friction}

1. A.Metal ball will reach the earth's surface earlier than the insulating ball
2. B.Both will reach the earth's surface simultaneously.
3. C.Insulating ball will reach the earth's surface earlier than the metal ball
4. D.Time taken by them to reach the earth's surface will be independent of the properties of their materials

A lift of mass $\mathrm{M}=500\text{ kg}$ is descending with speed of $2{\text{ ms}}^{-1}$. Its supporting cable begins to slip thus allowing it to fall with a constant acceleration of $2{\text{ ms}}^{-2}$. The kinetic energy of the lift at the end of fall through to a distance of $6\text{ m}$ will be ___________ kJ.

A body of mass $10\text{ kg}$ is moving with an initial speed of $20\text{ m/s}$. The body stops after $5\text{ s}$ due to friction between body and the floor. The value of the coefficient of friction is: (Take acceleration due to gravity $g=10{\text{ ms}}^{-2}$ )

1. A.$0.3$
2. B.$0.2$
3. C.$0.5$
4. D.$0.4$

A stone of mass $1\text{ kg}$ is tied to end of a massless string of length $1\text{ m}$. If the breaking tension of the string is $400\text{ N}$, then maximum linear velocity, the stone can have without breaking the string, while rotating in horizontal plane, is :

1. A.$20{\text{ ms}}^{-1}$
2. B.$40{\text{ ms}}^{-1}$
3. C.$400{\text{ ms}}^{-1}$
4. D.$10{\text{ ms}}^{-1}$

A small object at rest, absorbs a light pulse of power $20\mathrm{mW}$ and duration $300\mathrm{ns}$. Assuming speed of light as $3\times 10^{8}m/s$, the momentum of the object becomes equal to :

1. A.$1\times 10^{-17}\mathrm{kg}m/s$
2. B.$0.5\times 10^{-17}\mathrm{kg}m/s$
3. C.$3\times 10^{-17}\mathrm{kg}m/s$
4. D.$2\times 10^{-17}\mathrm{kg}m/s$

1. A.$0.25m/s$
2. B.$4m/s$
3. C.$0$
4. D.$2m/s$

1. A.b and c
2. B.c and a
3. C.a and b
4. D.c and b

A block of mass $m$ slides down the plane inclined at angle $30^{\circ }$ with an acceleration $\frac{g}{4}$. The value of coefficient of kinetic friction will be:

1. A.$\frac{2\sqrt{3}-1}{2}$
2. B.$\frac{\sqrt{3}}{2}$
3. C.$\frac{1}{2\sqrt{3}}$
4. D.$\frac{2\sqrt{3}+1}{2}$

A car is moving on a horizontal curved road with radius 50 m. The approximate maximum speed of car will be, if the coefficient of friction between tyres and road is 0.34. [take $g=10\mathrm{m}{\mathrm{s}}^{-2}$]

1. A.$3.4\mathrm{m}{\mathrm{s}}^{-1}$
2. B.$13\mathrm{m}{\mathrm{s}}^{-1}$
3. C.$22.4\mathrm{m}{\mathrm{s}}^{-1}$
4. D.$17\mathrm{m}{\mathrm{s}}^{-1}$

The time taken by an object to slide down $45^{\circ }$ rough inclined plane is n times as it takes to slide down a perfectly smooth $45^{\circ }$ incline plane. The coefficient of kinetic friction between the object and the incline plane is :

1. A.$1-\frac{1}{n^2}$
2. B.$1+\frac{1}{n^2}$
3. C.$\sqrt{1-\frac{1}{n^2}}$
4. D.$\sqrt{\frac{1}{1-n^2}}$

Consider a block kept on an inclined plane (incline at $45^{\circ }$) as shown in the figure. If the force required to just push it up the incline is 2 times the force required to just prevent it from sliding down, the coefficient of friction between the block and inclined plane$(\mu )$ is equal to :

1. A.0.60
2. B.0.33
3. C.0.25
4. D.0.50

Every planet revolves around the sun in an elliptical orbit :- A. The force acting on a planet is inversely proportional to square of distance from sun. B. Force acting on planet is inversely proportional to product of the masses of the planet and the sun. C. The Centripetal force acting on the planet is directed away from the sun. D. The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit. Choose the correct answer from the options given below :

1. A.C and D only
2. B.B and C only
3. C.A and D only
4. D.A and C only

1. A.$(4\sqrt{3}-1)\mathrm{N}$
2. B.$(4\sqrt{3}+1)\mathrm{N}$
3. C.$4(\sqrt{3}-1)\mathrm{N}$
4. D.$4(\sqrt{3}+1)\mathrm{N}$

1. A.
2. B.
3. C.
4. D.

1. A.$1.2\times 10^{-5}\mathrm{N}$ directed towards wire X.
2. B.$1.2\times 10^{-4}\mathrm{N}$ directed away from wire X.
3. C.$1.2\times 10^{-4}\mathrm{N}$ directed towards wire X.
4. D.$2.4\times 10^{-5}\mathrm{N}$ directed towards wire X.

1. A.$30\mathrm{N}$
2. B.$40\mathrm{N}$
3. C.$50\mathrm{N}$
4. D.$60\mathrm{N}$

If momentum of a body is increased by 20%, then its kinetic energy increases by

1. A.36%
2. B.40%
3. C.44%
4. D.48%

The velocity of a small ball of mass $0.3\mathrm{g}$ and density $8g/cc$ when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is $1.3g/cc$, then the value of viscous force acting on the ball will be $x\times 10^{-4}\mathrm{N}$. The value of $x$ is ____. [use $g=10m/{\mathrm{s}}^2$]

The speed of a transverse wave passing through a string of length $50\mathrm{cm}$ and mass $10\mathrm{g}$ is $60\mathrm{m}{\mathrm{s}}^{-1}$. The area of cross-section of the wire is $2.0\mathrm{m}{\mathrm{m}}^2$ and its Young's modulus is $1.2\times 10^{11}\mathrm{N}{\mathrm{m}}^{-2}$. The extension of the wire over its natural length due to its tension will be $x\times 10^{-5}\mathrm{m}$. The value of $x$ is ____.

The equation $\lambda =\frac{1.227}{x}\text{ nm}$ can be used to find the de-Brogli wavelength of an electron. In this equation $x$ stands for : Where $\text{m}=\text{mass of electron}$ $\text{P}=\text{momentum of electron}$ $\text{K}=\text{Kinetic energy of electron}$ $\text{V}=\text{Accelerating potential in volts for electron}$

1. A.$\sqrt{\text{mK}}$
2. B.$\sqrt{\text{P}}$
3. C.$\sqrt{\text{K}}$
4. D.$\sqrt{\text{V}}$

1. A.6
2. B.2
3. C.1.5
4. D.4

A bag is gently dropped on a conveyor belt moving at a speed of $2\text{ m/s}$. The coefficient of friction between the conveyor belt and bag is $0.4$. Initially, the bag slips on the belt before it stops due to friction. The distance travelled by the bag on the belt during slipping motion, is : [Take $g=10{\text{ m/s}}^2$ ]

1. A.$2\text{ m}$
2. B.$0.5\text{ m}$
3. C.$3.2\text{ m}$
4. D.$0.8\text{ m}$