Laws of Motion & Friction · JEE Main previous year questions

1. A.0.29 and $3.5\mathrm{m}$
2. B.0.29 and $6.5\mathrm{m}$
3. C.0.2 and $6.5\mathrm{m}$
4. D.0.2 and $3.5\mathrm{m}$

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

1. A.$120\mathrm{N}$
2. B.$150\mathrm{N}$
3. C.$100\mathrm{N}$
4. D.$80\mathrm{N}$

A block of mass $m$ is placed on a surface with a vertical cross section given by $y=\frac{x^3}{6}$. If the coefficient of friction is $0.5$, the maximum height above the ground at which the block can be placed without slipping is:

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

A bob of mass $m$ attached to an inextensible string of length $l$ is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed $\omega rad/s$ about the vertical. About the point of suspension:

1. A.angular momentum is conserved
2. B.angular momentum changes in magnitude but not in direction.
3. C.angular momentum changes in direction but not in magnitude.
4. D.angular momentum changes both in direction and magnitude.

1. A.$\frac{2g}{3}$
2. B.$\frac{g}{2}$
3. C.$\frac{5g}{6}$
4. D.$g$

A stone of mass $m$, tied to the end of a string, is whirled around in a circle on a horizontal frictionless table. The length of the string is reduced gradually keeping the angular momentum of the stone about the centre of the circle constant. Then, the tension in the string is given by $T=A{r}^n$, where $A$ is a constant, $r$ is the instantaneous radius of the circle. The value of $n$ is equal to

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

Currents of 10 ampere and 2 ampere are passed through two parallel thin wires $A$ and $B$ respectively in opposite directions. Wire $A$ is infinitely long and the length of the wire $B$ is $2\mathrm{m}$. The force acting on the conductor $B$, which is situated at $10\mathrm{cm}$ distance from $A$ will be

1. A.$8\times 10^{-5}\mathrm{N}$
2. B.$5\times 10^{-5}\mathrm{N}$
3. C.$8\pi \times 10^{-7}\mathrm{N}$
4. D.$4\pi \times 10^{-7}\mathrm{N}$

1. A.$\cot \alpha =3$
2. B.$\sec \alpha =3$
3. C.$\mathrm{cosec}\alpha =3$
4. D.$\cos \alpha =3$

1. A.$\frac{m_2}{m_1}$
2. B.$\frac{m_1}{m_2}$
3. C.$\sqrt{\frac{m_2}{m_1}}$
4. D.$\sqrt{\frac{m_1}{m_2}}$

A solid sphere having mass $m$ and radius $r$ rolls down an inclined plane. Then its kinetic energy is

1. A.$\frac{5}{7}$ rotational and $\frac{2}{7}$ translational
2. B.$\frac{2}{7}$ rotational and $\frac{5}{7}$ translational
3. C.$\frac{2}{5}$ rotational and $\frac{3}{5}$ translational
4. D.$\frac{1}{2}$ rotational and $\frac{1}{2}$ translational

1. A.$4.9\mathrm{m}{\mathrm{s}}^{-2}$ in horizontal direction
2. B.$9.8\mathrm{m}{\mathrm{s}}^{-2}$ in vertical direction
3. C.Zero
4. D.$4.9\mathrm{m}{\mathrm{s}}^{-2}$ in vertical direction

The equation of a wave on a string of linear mass density $0.04\mathrm{kg}{\mathrm{m}}^{-1}$ is given by $$y=0.02(\mathrm{m})\sin \left[2\pi \left(\frac{t}{0.04(\mathrm{s})}-\frac{x}{0.50(\mathrm{m})}\right)\right].$$ The tension in the string is

1. A.$4.0\mathrm{N}$
2. B.$12.5\mathrm{N}$
3. C.$0.5\mathrm{N}$
4. D.$6.25\mathrm{N}$

A mass of $Mkg$ is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle of $45^{\circ }$ with the initial vertical direction is

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

A wire elongates by $lmm$ when a LOAD $W$ is hanged from it. If the wire goes over a pulley and two weights $W$ each are hung at the two ends, the elongation of the wire will be (in $mm$)

1. A.$l$
2. B.$2l$
3. C.zero
4. D.$l/2$

A string is stretched between fixed points separated by $75.0cm$. It is observed to have resonant frequencies of $420Hz$ and $315Hz$. There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is

1. A.$105Hz$
2. B.$1.05Hz$
3. C.$1050Hz$
4. D.$10.5Hz$

A parachutist after bailing out falls $50m$ without friction. When parachute opens, it decelerates at $2m/s^2$. He reaches the ground with a speed of $3m/s$. At what height, did he bail out?

1. A.$182m$
2. B.$91m$
3. C.$111m$
4. D.$293m$

The upper half of an inclined plane with inclination $\varphi$ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by

1. A.$2\cos \varphi$
2. B.$2\sin \varphi$
3. C.$\tan \varphi$
4. D.$2\tan \varphi$

1. A.$g\mathrm{cosec}\alpha$
2. B.$g/\tan \alpha$
3. C.$g\tan \alpha$
4. D.$g$

1. A.$\frac{k{L}^2}{2M}$
2. B.$\sqrt{Mk}L$
3. C.$\frac{M{L}^2}{k}$
4. D.$\mathrm{Zero}$

Two masses $m_1=5\mathrm{kg}$ and $m_2=4.8\mathrm{kg}$ tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when left free to move? $(g=9.8m/{\mathrm{s}}^2)$

1. A.$5m/{\mathrm{s}}^2$
2. B.$9.8m/{\mathrm{s}}^2$
3. C.$0.2m/{\mathrm{s}}^2$
4. D.$4.8m/{\mathrm{s}}^2$

A block rests on a rough inclined plane making an angle of $30^{\circ }$ with the horizontal. The coefficient of static friction between the block and the plane is $0.8$. If the frictional force on the block is $10\mathrm{N}$, the mass of the block (in $\mathrm{kg}$) is $(takeg=10m/{\mathrm{s}}^2)$

1. A.$1.6$
2. B.$4.0$
3. C.$2.0$
4. D.$2.5$

A radiation of energy $E$ falls normally on a perfectly reflecting surface. The momentum transferred to the surface is

1. A.$Ec$
2. B.$2E/c$
3. C.$E/c$
4. D.$E/c^2$

A lift is moving down with acceleration $a$. A man in the lift drops a ball inside the lift. The acceleration of the ball as observed by the man in the lift and a man standing stationary on the ground are respectively

1. A.$g,g$
2. B.$g-a,g-a$
3. C.$g-a,g$
4. D.$a,g$

A light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ (vertically). If the acceleration of the system is $g/8$, then the ratio of the masses is

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