Laws of Motion & Friction · JEE Main previous year questions

A body of mass $m$ is suspended by two strings making angles ${\theta }_1$ and ${\theta }_2$ with the horizontal ceiling with tensions $T_1$ and $T_2$ simultaneously. $T_1$ and $T_2$ are related by $T_1=\sqrt{3}{T}_2$, the angles ${\theta }_1$ and ${\theta }_2$ are

1. A.${\theta }_1=30^{\circ }{\theta }_2=60^{\circ }\text{ with }{T}_2=\frac{3mg}{4}$
2. B.${\theta }_1=45^{\circ }{\theta }_2=45^{\circ }\text{ with }{T}_2=\frac{3mg}{4}$
3. C.${\theta }_1=30^{\circ }{\theta }_2=60^{\circ }\text{ with }{T}_2=\frac{4mg}{5}$
4. D.${\theta }_1=60^{\circ }{\theta }_2=30^{\circ }\text{ with }{T}_2=\frac{mg}{2}$

A circular ring and a solid sphere having same radius roll down on an inclined plane from rest without slipping. The ratio of their velocities when reached at the bottom of the plane is $\sqrt{\frac{x}{5}}$ where $x=$ ____.

A block of mass $25\mathrm{kg}$ is pulled along a horizontal surface by a force at an angle $45^{\circ }$ with the horizontal. The friction coefficient between the block and the surface is 0.25 . The block travels at a uniform velocity. The work done by the applied force during a displacement of $5\mathrm{m}$ of the block is :

1. A.$490\mathrm{J}$
2. B.$970\mathrm{J}$
3. C.$735\mathrm{J}$
4. D.$245\mathrm{J}$

A block of mass $1\mathrm{kg}$, moving along $x$ with speed $v_i=10m/s$ enters a rough region ranging from $x=0.1\mathrm{m}$ to $x=1.9\mathrm{m}$. The retarding force acting on the block in this range is ${\mathrm{F}}_{\mathrm{r}}=-kx\mathrm{N}$, with $k=10N/m$. Then the final speed of the block as it crosses rough region is.

1. A.$4m/s$
2. B.$10m/s$
3. C.$8m/s$
4. D.$6m/s$

1. A.$1.77{\text{ nC/m}}^2$
2. B.$0.885{\text{ nC/m}}^2$
3. C.$885{\text{ nC/m}}^2$
4. D.$17.7{\text{ nC/m}}^2$

1. A.$5\sqrt{3},5$
2. B.$5\sqrt{3},5\sqrt{3}$
3. C.$5,5$
4. D.$5,5\sqrt{3}$

The length of a light string is 1.4 m when the tension on it is 5 N . If the tension increases to 7 N , the length of the string is 1.56 m . The original length of the string is__________m.

1. A.$\sqrt{2Rg+\frac{k{R}^2}{m}}$
2. B.$\sqrt{3Rg+\frac{k{R}^2}{m}}$
3. C.$\sqrt{2Rg+\frac{4k{R}^2}{m}}$
4. D.$2\sqrt{gR+\frac{k{R}^2}{m}}$

A car of mass ' $m$ ' moves on a banked road having radius ' $r$ ' and banking angle $\theta$. To avoid slipping from banked road, the maximum permissible speed of the car is $v_0$. The coefficient of friction $\mu$ between the wheels of the car and the banked road is

1. A.$\mu =\frac{v_0^2+rg\tan \theta }{rg+v_0^2\tan \theta }$
2. B.$\mu =\frac{v_0^2-rg\tan \theta }{rg-v_0^2\tan \theta }$
3. C.$\mu =\frac{v_0^2-rg\tan \theta }{rg+v_0^2\tan \theta }$
4. D.$\mu =\frac{v_0^2+rg\tan \theta }{rg-v_0^2\tan \theta }$

The energy E and momentum p of a moving body of mass m are related by some equation. Given that c represents the speed of light, identify the correct equation

1. A.${\mathrm{E}}^2={\mathrm{pc}}^2+{\mathrm{m}}^2{\mathrm{c}}^4$
2. B.${\mathrm{E}}^2={\mathrm{pc}}^2+{\mathrm{m}}^2{\mathrm{c}}^2$
3. C.${\mathrm{E}}^2={\mathrm{p}}^2{\mathrm{c}}^2+{\mathrm{m}}^2{\mathrm{c}}^4$
4. D.${\mathrm{E}}^2={\mathrm{p}}^2{\mathrm{c}}^2+{\mathrm{m}}^2{\mathrm{c}}^2$

A solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be $t_1$ and $t_2$, respectively, then

1. A.$t_1<t_2$
2. B.$t_1=2t_2$
3. C.$t_1>t_2$
4. D.$t_1=t_2$

The equation of a transverse wave travelling along a string is $y(x,t)=4.0\sin \left[20\times 10^{-3}x+600t\right]\text{mm}$, where $x$ is in $\text{mm}$ and $t$ is in second. The velocity of the wave is :

1. A.$-60\text{ m/s}$
2. B.$+60\text{ m/s}$
3. C.$+30\text{ m/s}$
4. D.$-30\text{ m/s}$

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

A light unstretchable string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$. If the acceleration of the system is $\frac{g}{8}$, then the ratio of the masses $\frac{m_2}{m_1}$ is :

1. A.$5:3$
2. B.$8:1$
3. C.$9:7$
4. D.$4:3$

A circular disc reaches from top to bottom of an inclined plane of length $l$. When it slips down the plane, it takes $t\mathrm{s}$. When it rolls down the plane then it takes ${\left(\frac{\alpha }{2}\right)}^{1/2}t\mathrm{s}$, where $\alpha$ is ____.

1. A.$\sqrt{6}\mathrm{m}$
2. B.$\sqrt{5}\mathrm{m}$
3. C.$1\mathrm{m}$
4. D.$2\mathrm{m}$

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

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

A car of $800\mathrm{kg}$ is taking turn on a banked road of radius $300\mathrm{m}$ and angle of banking $30^{\circ }$. If coefficient of static friction is 0.2 then the maximum speed with which car can negotiate the turn safely: $(g=10m/{\mathrm{s}}^2,\sqrt{3}=1.73)$

1. A.$51.4m/s$
2. B.$102.8m/s$
3. C.$70.4m/s$
4. D.$264m/s$

When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be :

1. A.60%
2. B.500%
3. C.6%
4. D.600%

A heavy box of mass $50\mathrm{kg}$ is moving on a horizontal surface. If co-efficient of kinetic friction between the box and horizontal surface is 0.3 then force of kinetic friction is :

1. A.$1470\mathrm{N}$
2. B.$147\mathrm{N}$
3. C.$1.47\mathrm{N}$
4. D.$14.7\mathrm{N}$

A $2\text{ kg}$ brick begins to slide over a surface which is inclined at an angle of $45^{\circ }$ with respect to horizontal axis. The co-efficient of static friction between their surfaces is:

1. A.1
2. B.1.7
3. C.0.5
4. D.$\frac{1}{\sqrt{3}}$

1. A.1.2
2. B.4
3. C.3
4. D.2

1. A.4.5 kg
2. B.6.5 kg
3. C.9 kg
4. D.2.25 kg

1. A.$5\sqrt{3}N$
2. B.$\frac{5\sqrt{3}}{2}N$
3. C.$10\mathrm{N}$
4. D.$25\sqrt{3}N$