Laws of Motion & Friction · JEE Main previous year questions

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

When a body slides down from rest along a smooth inclined plane making an angle of $30^{\circ }$ with the horizontal, it takes time T. When the same body slides down from the rest along a rough inclined plane making the same angle and through the same distance, it takes time $\alpha \mathrm{T}$, where $\alpha$ is a constant greater than 1. The co-efficient of friction between the body and the rough plane is $\frac{1}{\sqrt{x}}\left(\frac{{\alpha }^2-1}{{\alpha }^2}\right)$ where x = ____.

1. A.$125\text{ cm}$
2. B.$1250\text{ cm}$
3. C.$12.5\text{ cm}$
4. D.$1.25\text{ cm}$

Two waves are simultaneously passing through a string and their equations are : $y_1=A_1\sin k(x-vt)$, $y_2=A_2\sin k(x-vt+x_0)$. Given amplitudes $A_1=12\text{ mm}$ and $A_2=5\text{ mm}$, $x_0=3.5\text{ cm}$ and wave number $k=6.28{\text{ cm}}^{-1}$. The amplitude of resulting wave will be ............... mm.

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

A porter lifts a heavy suitcase of mass $80\text{ kg}$ and at the destination lowers it down by a distance of $80\text{ cm}$ with a constant velocity. Calculate the work done by the porter in lowering the suitcase. (take $g=9.8{\text{ ms}}^{-2}$)

1. A.$+627.2\text{ J}$
2. B.$-62720.0\text{ J}$
3. C.$-627.2\text{ J}$
4. D.$784.0\text{ J}$

A bullet of '$4\text{ g}$' mass is fired from a gun of mass $4\text{ kg}$. If the bullet moves with the muzzle speed of $50{\text{ ms}}^{-1}$, the impulse imparted to the gun and velocity of recoil of gun are :

1. A.$0.2{\text{ kg ms}}^{-1},0.1{\text{ ms}}^{-1}$
2. B.$0.4{\text{ kg ms}}^{-1},0.05{\text{ ms}}^{-1}$
3. C.$0.2{\text{ kg ms}}^{-1},0.05{\text{ ms}}^{-1}$
4. D.$0.4{\text{ kg ms}}^{-1},0.1{\text{ ms}}^{-1}$

A circular disc reaches from top to bottom of an inclined plane of length 'L'. When it slips down the plane, it makes time '$t_1$'. When it rolls down the plane, it takes time $t_2$. The value of $\frac{t_2}{t_1}$ is $\sqrt{\frac{3}{x}}$. The value of x will be ________.

A rod of mass M and length L is lying on a horizontal frictionless surface. A particle of mass 'm' travelling along the surface hits at one end of the rod with a velocity 'u' in a direction perpendicular to the rod. The collision is completely elastic. After collision, particle comes to rest. The ratio of masses $\left(\frac{m}{M}\right)$ is $\frac{1}{x}$. The value of 'x' will be ________.

1. A.0
2. B.$5mg$
3. C.$\frac{7}{2}mg$
4. D.$\frac{mg}{5}$

1. A.$\frac{F}{m}\cos \theta +{\mu }_k\left(g-\frac{F}{m}\sin \theta \right)$
2. B.$\frac{F}{m}\cos \theta -{\mu }_k\left(g-\frac{F}{m}\sin \theta \right)$
3. C.$-\frac{F}{m}\cos \theta -{\mu }_k\left(g-\frac{F}{m}\sin \theta \right)$
4. D.$\frac{F}{m}\cos \theta -{\mu }_k\left(g+\frac{F}{m}\sin \theta \right)$

A person standing on a spring balance inside a stationary lift measures 60 kg. The weight of that person if the lift descends with uniform downward acceleration of $1.8m/{\mathrm{s}}^2$ will be _________ N. $[\mathrm{g}=10m/{\mathrm{s}}^2]$

1. A.$\frac{v_0^2}{2g\sin \theta }$
2. B.$\frac{7v_0^2}{10g\sin \theta }$
3. C.$\frac{2}{5}\frac{v_0^2}{g\sin \theta }$
4. D.$\frac{v_0^2}{5g\sin \theta }$

The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by 4%, will be __________%.

Two identical conducting spheres with negligible volume have 2.1 nC and $-0.1\text{ nC}$ charges, respectively. They are brought into contact and then separated by a distance of 0.5 m. The electrostatic force acting between the spheres is ______ $\times 10^{-9}\text{ N}$. $[\text{Given : }4\pi {\epsilon }_0=\frac{1}{9\times 10^9}\text{ SI unit}]$

Two particles having masses 4 g and 16 g respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is n : 2. The value of n will be ___________.

An insect is at the bottom of a hemispherical ditch of radius $1\text{ m}$. It crawls up the ditch but starts slipping after it is at height h from the bottom. If the coefficient of friction between the ground and the insect is 0.75, then h is : $(g=10\mathrm{m}{\mathrm{s}}^{-2})$

1. A.$0.45\text{ m}$
2. B.$0.60\text{ m}$
3. C.$0.20\text{ m}$
4. D.$0.80\text{ m}$

Given the masses of various atomic particles $m_p=1.0072\text{ u}$, $m_n=1.0087\text{ u}$, $m_e=0.000548\text{ u}$, $m_{\bar{\nu }}=0$, $m_d=2.0141\text{ u}$, where $\mathrm{p}\equiv \mathrm{proton}$, $\mathrm{n}\equiv \mathrm{neutron}$, $\mathrm{e}\equiv \mathrm{electron}$, $\bar{\nu }\equiv \text{antineutrino}$ and $\mathrm{d}\equiv \mathrm{deuteron}$. Which of the following process is allowed by momentum and energy conservation?

1. A.$\mathrm{n}+\mathrm{n}\to \text{deuterium atom}$ (electron bound to the nucleus)
2. B.$\mathrm{n}+\mathrm{p}\to \mathrm{d}+\gamma$
3. C.$\mathrm{p}\to \mathrm{n}+{\mathrm{e}}^{+}+\bar{\nu }$
4. D.${\mathrm{e}}^{+}+{\mathrm{e}}^{-}\to \gamma$

1. A.$63^{\circ }$
2. B.$69^{\circ }$
3. C.$55^{\circ }$
4. D.$49^{\circ }$

A block starts moving up an inclined plane of inclination $30^{\circ }$ with an initial velocity of $v_0$. It comes back to its initial position with velocity $\frac{v_0}{2}$. The value of the coefficient of kinetic friction between the block and the inclined plane is close to $\frac{I}{1000}$. The nearest integer to I is _______.