Second Law of Motion

Q. A uniform rod of length $200\text{cm}$ and mass $500\text{g}$ is balanced on a wedge placed at $40\text{cm}$ mark. A mass of $2\text{Kg}$ is suspended from the rod at $20\text{cm}$ and another unknown mass ${}^{\prime }{m}^{\prime }$ is suspended from the rod at $160\text{cm}$ mark as shown in the figure. Find the value of $m$ such that the rod is in equilibrium.
$(g=10{\text{ms}}^{-2})$

1. $\frac{1}{2}\text{Kg}$
2. $\frac{1}{3}\text{Kg}$
3. $\frac{1}{6}\text{Kg}$
4. $\frac{1}{12}\text{Kg}$

Q. Two point charges $Q_1$ and $Q_2$ exerts force $F$ on each other, when kept at certain distance apart. If the charge on each particle is halved and the distance between them is doubled, then the new force between the two particles would be

1. $\frac{F}{2}$
2. $\frac{F}{4}$
3. $\frac{F}{8}$
4. $\frac{F}{16}$

Q.

A parachutist with total weight 75 kg drops vertically onto a sandy ground with a speed of 2 ms${}^{-1}$ and comes to a halt over a distance of 0.25m. The average force from the ground on her is close to.

1. 600 N

2. 1200 N

3. 1350 N

4. 1950 N

Q. Two-point charges $Q_1$ and $Q_2$ are $3\text{m}$ apart and their combined charge is $20\mu \text{C}$. If one repels the other with force of $0.075\text{N}$. Calculate the two charges. (in $\mu \text{C}$)

1. $15,5$
2. $10,10$
3. $35,-15$
4. $25,-5$

Q.

A body of mass 2kg is moving with an acceleration of 50cm s^-1 calculate the force acting

Q. An object of mass $3\text{kg}$ is sliding with a constant velocity of $1\text{m/s}$ on a frictionless horizontal table, the external force required to keep the object moving with the same velocity is

1. $30\text{N}$
2. $0\text{N}$
3. $20\text{N}$
4. $10\text{N}$

Q. A stone is thrown vertically upwards with an initial velocity of $25\text{m/s}$. The maximum height reached by the stone is
$[$Take $g=10{\text{m/s}}^2]$

1. $11.5\text{m}$
2. $20.15\text{m}$
3. $31.25\text{m}$
4. $5.75\text{m}$

Q. A ball is thrown upward with an initial velocity $v_o$ from the surface of the earth. The motion of the ball is affected by a drag force equal to $m\gamma v^2$ (where, $m$ is mass of the ball, $v$ is its instantaneous velocity and $\gamma$ is a constant). Time taken by the ball to rise to its zenith (maximum height) is

1. $\frac{1}{\sqrt{2}\gamma g}{\tan }^{-1}\left(\sqrt{\frac{2\gamma }{g}}{v}_0\right)$
2. $\frac{1}{\sqrt{\gamma g}}{\tan }^{-1}\left(\sqrt{\frac{\gamma }{g}}{v}_0\right)$
3. $\frac{1}{\sqrt{\gamma g}}\ln (1+\sqrt{\frac{\gamma }{g}}{v}_0)$
4. $\frac{1}{\sqrt{\gamma g}}{\sin }^{-1}\left(\sqrt{\frac{\gamma }{g}}{v}_0\right)$

Q.

A ball of mass (m) 0.5 kg is attached to the end of a string having length (l) 0.5m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N. The maximum possible value of angular velocity of ball (in rad/s) is

1. 9

2. 18

3. 27

4. 36

Q.

Explain why some of the leaves may get detached from a tree if we vigorously shake its branch.

Q.

If the net force acting on a body be zero, then will the body remain necessarily in rest position?

Q. A monkey of mass $20\text{kg}$ is holding a vertical rope. The rope will not break when a mass of $25\text{kg}$ is suspended from it but will break if the mass exceeds $25\text{kg}$. What is the maximum acceleration with which the monkey can climb up along the rope? $g=10{\text{m/s}}^2)$

1. $5{\text{m/s}}^2$
2. $25{\text{m/s}}^2$
3. $10{\text{m/s}}^2$
4. $2.5{\text{m/s}}^2$

Q. An inclined plane making an angle of ${30}^{\circ }$ with the horizontal is placed in a uniform horizontal electric field $200\text{N/C}$ as shown in the figure. A body of mass $1\text{kg}$ and charge $5\text{mC}$ is allowed to slide down from rest from a height of $1\text{m}$. If the coefficient of friction is $0.2$, find the time taken by the body to reach the bottom.

$[g=9.8{\text{m/s}}^2;\sin {30}^{\circ }=\frac{1}{2};\cos {30}^{\circ }=\frac{\sqrt{3}}{2}]$

1. $2.3\text{s}$
2. $0.46\text{s}$
3. $1.3\text{s}$
4. $0.92\text{s}$

Q.

What is momentum? Explain with examples.

Q. A particle moves in the $x-y$ plane under the influence of a force such that its linear momentum is $\overrightarrow{p}\left(t\right)=A\left[\cos \right(kt)\hat{i}-\sin (kt\left)\hat{j}\right]$, where $A$ and $k$ are constants. The angle between the force and the momentum is :

1. ${45}^{\circ }$
2. ${90}^{\circ }$
3. $0^{\circ }$
4. ${30}^{\circ }$

Q. A length $L$ of wire carries a current $i$. If the wire is formed into a circular coil, then the maximum torque in a given magnetic field is developed when the coil has one turn only. Find the magnitude of maximum torque.

1. $\frac{iLB}{2\pi }$
2. $\frac{i{L}^{2}B}{\pi }$
3. $\frac{i{L}^{2}B}{4{\pi }^2}$
4. $\frac{i{L}^{2}B}{2\pi }$

Q. A marble block of mass $2kg$ lying on ice when given a velocity of $6m/s$ is stopped by friction in $10s$. Then the coefficient of friction is

1. $0.02$
2. $0.06$
3. $0.01$
4. $0.03$

Q. Reading shown in two spring balances $S_1\text{and}{S}_2$ is $90\text{kg}$ and $30\text{kg}$ respectvely and lift is accelerating upwards with acceleration $10\frac{m}{s^2}.\text{If}{S}_1$ is elongated and $S_2$ is compressed and mass is stationary with respect to lift, then the mass of the block will be

1. $60\text{kg}$
2. $30\text{kg}$
3. None of these
4. $120\text{kg}$

Q. Gravel is dropped into a conveyor belt at the rate of $0.5kg/s$. Find the extra force required to keep the belt moving at $2m/s$.

1. $1N$
2. $2N$
3. $4N$
4. $5N$

Q. A body of mass $2kg$ makes an elastic collision with a second body at rest and continues to move in the original direction but with one fourth of its original speed. What is the mass of the second body?

1. $1.8kg$
2. $1.0kg$
3. $1.2kg$
4. $1.5kg$

Q.

A motorcar of mass $1200$ kg is moving along a straight line with a uniform velocity of $90$ km/h. Its velocity is slowed down to $18$ km/h in $4$ s by an unbalanced external force. Calculate the acceleration and change in momentum. Also calculate the magnitude of the force required?

Q. A monkey of 4 kg mass is climbing up on rope with v=$4t^2$, find tension in rope at t=5 sec.

1. 120 N
2. 160 N
3. 200 N
4. 40 N

Q.

A rocket with a lift-off mass $3.5\times {10}^{4}kg$ is blasted upwards with an initial acceleration of $10m/s^2$. Then the initial thrust of the blast is

1. 

2. 

3. 

4. 

Q.

What does a bowler tend to gain during running from a long distance he bowls from the take-off line.

Q. Two blocks each of masses $m$ lie on a smooth table. They are attached to two other masses as shown in figure. The pulleys and strings are light. An object $\text{O}$ is kept at rest on the table and the sides $\text{AB}$ and $\text{CD}$ of the two blocks are made reflecting. The acceleration of the images formed in these two reflecting surfaces with respect to each other is:

1. $\frac{5g}{6}$
2. $\frac{g}{3}$
3. $\frac{17g}{12}$
4. $\frac{17g}{6}$

Q. In the figure given below, the position-time graph of a particle of mass 0.1 Kg is shown. The impulse at t = 2 sec is

1. 
2. 
3. 
4. 

Q.

How do you calculate the force needed to move a car?

Q.

What causes motion?

Q. A gas of density $\rho$ flows with velocity $v$ along a pipe of cross - sectional area $S$ and bent to an angle of ${90}^{\circ }$ at point $A$. What force does the gas exert on the pipe at point $A$ ?

1. $\sqrt{7}S{v}^2\rho$
2. $\sqrt{3}S{v}^2\rho$
3. $\sqrt{5}S{v}^2\rho$
4. $\sqrt{2}S{v}^2\rho$

Q. An impulse $J$ is applied on a ring of mass $m$ along a line passing through its centre $O$. The ring is placed on a rough horizontal surface. The linear velocity of centre of ring once it starts rolling without slipping is

1. $J/4m$
2. $J/2m$
3. $J/m$
4. $J/3m$