Newton's Laws for System of Particles

Q.

Which of the following are vectors and which are scalars: Distance, mass, time, weight, volume, density, speed, velocity, acceleration, force, temperature and energy?

Q.

Deuteron and alpha particles are put $1\stackrel{o}{A}$ apart in the air. The magnitude of the intensity of the electric field due to deuteron on the alpha particle is (N/C)

1. Zero

2. $2.88\times {10}^{-11}\frac{\text{N}}{\text{C}}$

3. $1.44\times {10}^{-11}\frac{\text{N}}{\text{C}}$

4. $5.76\times {10}^{-11}\frac{\text{N}}{\text{C}}$

Q. Derive the relation between momentum and impulse

Q. A particle $\text{A}$ of mass $m_A=\frac{m}{2}$ moving along the $x-$axis with velocity $v_0$ collides elastically with another particle $\text{B}$ at rest having mass $m_B=\frac{m}{3}$. If both particle move along the $x-$ axis after the collision. The change $\Delta \lambda$ in de-Broglie wavelength of particle $\text{A}$, in terms of its de-Broglie wavelength $\left({\lambda }_0\right)$ before collision is-

1. $\Delta \lambda =\frac{3}{2}{\lambda }_0$
2. $\Delta \lambda =\frac{5}{2}{\lambda }_0$
3. $\Delta \lambda =2{\lambda }_0$
4. $\Delta \lambda =4{\lambda }_0$

Q.

A hockey ball of mass $200g$ travelling at $10m.s^{-1}$ is struck by a hockey stick so as to return it along its original path with a velocity at $5m.s^{-1}$. Calculate the change of momentum that occurred in the motion of the hockey ball by the force applied by the hockey stick.

Q. Consider the pulley-block system shown in the figure below. If the system is released from rest, then identify the correct statement regarding acceleration of the centre of mass of the system. Assume $M\ne m$.

1. It is in vertically downward direction.
2. The direction of acceleration of centre of mass depends on which mass is greater.
3. The centre of mass does not accelerate.
4. It is in vertically upward direction.

Q. A semicircular portion of radius $r$ is cut from a uniform rectangular plate as shown in figure. The distance of centre of mass $\text{C}$ of remaining plate, from point $\text{O}$ is

1. $\frac{2r}{(3-\pi )}$
2. $\frac{3r}{2(4-\pi )}$
3. $\frac{2r}{(4+\pi )}$
4. $\frac{2r}{3(4-\pi )}$

Q. A piece of wood of mass $0.03\text{kg}$ is dropped from the top of a 100 m height building. At the same time, a bullet of mass $0.02\text{kg}$ is fired vertically upward with a velocity $100{\text{ms}}^{-1}$ from the ground. The bullet after collision gets embedded in the wood. Then, the maximum height to which the combined system reaches above the top of the building before falling below is $\text{Take, g}=10m{s}^{-2})$

1. $30\text{m}$
2. $20\text{m}$
3. $10\text{m}$
4. $40\text{m}$

Q.

A small body of superdense material, whose mass is twice the mass of the earth but whose size is very small compared to the size of the earth, starts from rest at a height H<<R above the earths surface, and reaches the earths surface in time t. Then t is equal to

1. 

2. 

3. 

4. 

Q.

A particle of mass m moves with constant speed v on a circular path of radius r. Find the magnitude of average force on it in half revolution.

Q. Give reason
it is easier to catch a tennis ball than a cricket ball even when both are moving on same velocity

Q. From the circular disc of radius $4R$, two small discs of radius $R$ are cut off. The centre of mass of the new structure will be at

1. $\frac{R}{5}(\hat{i}+\hat{j})$
2. $\frac{R}{5}(\hat{i}-\hat{j})$
3. $-\frac{3R}{14}(\hat{i}+\hat{j})$
4. $\frac{3R}{14}(\hat{i}+\hat{j})$

Q.

The moment of inertia of a uniform rod of mass 0.50 kg and length 1 m is 0.10 ${\text{kg-m}}^2$ about a line perpendicular to the rod. Find the distance of this line from the middle point of the rod.

Q. A tunnel is dug in the earth across one of the diameter. Two masses m and 2m are dropped from two ends of tunnel. The masses collide and stick each other. They perform SHM amplitude of which is

Q. Find the distance of centre of mass of a uniform plate having semicircular inner and outer boundaries of radii $a$ and $b$ from the centre $\text{O}$.

1. $\frac{2(b^2+a^2+ab)}{3\pi (a+b)}$
2. $\frac{4(b^2+a^2+ab)}{3\pi (a+b)}$
3. $\frac{3\pi (b^2+a^2+ab)}{4(a+b)}$
4. $\frac{4(b^2+a^2+ab)}{3\pi (a+b)}$

Q. Which of the following is/are correct?

1. If centre of mass of three particles is at rest and it is known that two of them are moving along different lines, then the third particle must also be moving.
2. If centre of mass remains at rest, then net work done by the forces acting on the system must be zero.
3. If centre of mass remains at rest, then the net external force must be zero.
4. Internal forces cannot change KE of system.

Q.

a body whose mass is 6 kg is acted on by a force which changes its velocity from 3 M per second to 5 M per second find the Impulse of Force.if force is active for 2 seconds find the force in Newtons .

Q.

A bomb of mass $10kg$ explodes into $2$ pieces of mass $4kg$ and $6kg$. The velocity of mass $4kg$ is $1.5m/s$, the K.E. of mass $6kg$ is ....…

1. $3.84J$

2. $9.6J$

3. $3J$

4. $2.5J$

Q. A uniform rod of length L and mass m is placed on rough horizontal surface.If coefficient of friction is $\mu =kx$, where k is constant and $\mu$ exist for $0\le x\le L$ (i.e for $x>L$ friction is zero.). If rod moves towards the right, magnitude of work done by friction is:

1. $\frac{kmg{L}^2}{3}$
2. $\frac{2kmg{L}^2}{3}$
3. $\frac{kmg{L}^2}{6}$
4. $\frac{kmg{L}^2}{9}$

Q.

The dipole moment of H₂O is 1.85D.HOH angle is 105°. O-H bond length is 0.94A˚. The magnitude of charge-separated on the oxygen atom is (cos 52.5° − 0.61)

1. 1/2 of the magnitude of the charge on the electron

2. 1/3 of the magnitude of the charge on the electron

3. 1/4 of the magnitude of the charge on the electron

4. 2/3 of the magnitude of the charge on the electron.

Q.

A ball of mass 50 g moving at a speed of 2.0 m/s strikes a plane surface at an angle of incidence ${45}^{\circ }$.The ball is reflected by the plane at equal angle of reflection with the same speed.Calculate (a) the magnitude of the change in momentum of the ball (b) the change in the magnitude of the momentum of the ball.

Q.

A scooter weighing 150 kg together with its rider moving at 36 km/hr is to take a turn of radius 30 m. What horizontal force on the scooter is needed to make the turn possible ?

Q. Two bodies A and B of masses 5 kg and 10 kg moving in free space in opposite directions with velocity 4 m/s and 0.5 m/s undergo head on collision. The force F of their mutual interaction varies with time t according to given graph. We can conclude

1. Period of deformation is 0.2 sec
2. At the time of maximum deformation speed of 5 kg is 1 m/s
3. Coefficient of restitution is 0.5
4. Speed of 10 kg after collision is 1.75 m/s

Q. A pulley-block system as shown in the figure is released from rest. What is the magnitude of acceleration of $\text{COM}$ of pulley-block system? (Take $g=10{\text{m/s}}^2$)

1. $5{\text{m/s}}^2$
2. $7{\text{m/s}}^2$
3. $10.5{\text{m/s}}^2$
4. $3.77{\text{m/s}}^2$

Q. A rod of negligible mass having length $l=2\text{m}$ is pivoted at its center and two masses, $6\text{kg}$ and $4\text{kg}$ are hung from the ends as shown in the figure. Find the initial angular acceleration of the rod if it is suddenly released from the horizontal position.



Take $g=10{\text{m/s}}^2$

1. $2{\text{rad/s}}^2$
2. $3{\text{rad/s}}^2$
3. $4{\text{rad/s}}^2$
4. $5{\text{rad/s}}^2$

Q.

What happens to the kinetic energy of an object if its velocity is doubled? Explain.

Q. Two blocks of masses $10kg$ and $30kg$ are placed on the same straight line with coordinates $(0,0)cm$ and $(x,0)cm$ respectively. The block of $10kg$ is moved on the same line through a distance of $6cm$ towards the other block. The distance through which the block of $30kg$ must be moved to keep the position of centre of mass of the system unchanged is

Q.

where does the center of mass of a two particle system lie when one particle is more massive than the other?

Q.

If the speed of a vehicle increases by 2 m/s, its kinetic energy is doubled. Then, the original speed of the vehicle is

1. $(\sqrt{2}+1)\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

2. $\sqrt{2}\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

3. $2(\sqrt{2}+1)\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

4. $\sqrt{2}(\sqrt{2}+1)\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Q. Two particles of masses $m$ and $2m$ start moving from origin with same constant speed along $x$ and $y$ axis respectively. The centre of mass of system of particles will move along the line

1. $y=3x$
2. $y=\frac{2x}{5}$
3. $y=2x$
4. $3y=x$