Equations of Motion

Q. A block of mass $m$ slides down on an inclined wedge of same mass $m$ as shown in figure. Friction is absent everywhere. Acceleration of center of mass of the block and wedge is

1. zero
2. $\frac{g{\sin }^2\theta }{(1+{\sin }^2\theta )}$
3. $\frac{g{\cos }^2\theta }{(1+{\sin }^2\theta )}$
4. $\frac{g\sin \theta }{(1+\cos \theta )}$

Q. A body of mass $10\text{kg}$ is moving with a constant velocity $10\text{m/s}$. When a constant force acts for $4\text{s}$ on it, it moves with a velocity $2\text{m/s}$ in the opposite direction. The magnitude of force acting on the body is

1. $30\text{N}$
2. $10\text{N}$
3. $45\text{N}$
4. $50\text{N}$

Q. A body of mass $2kg$ has an initial speed of $5m/s$. A force acts on it for some time in the direction of motion. The force-time graph is shown in the figure. The final speed of the body is

1. $9.25m/s$
2. $5m/s$
3. $14.25m/s$
4. $4.25m/s$

Q. An object of mass $10kg$ moves at a constant speed of $10m{s}^{-1}$. A constant force that acts for $4s$ on the object gives it a speed of $2m{s}^{-1}$ in the opposite direction. The magnitude of force acting on the object is (Take the direction of initial velocity as positive)

1. $3N$
2. $30N$
3. $300N$
4. $0.3N$

Q. An elevator and its load have a total mass of $800\text{kg}$. If the elevator, originally moving downward at $10\text{m/s}$, is brought to rest with constant deceleration in a distance of $25\text{m}$, the tension in the supporting cable will be ($g=10{\text{m/s}}^2$)

1. $8000\text{N}$
2. $11200\text{N}$
3. $9600\text{N}$
4. $6500\text{N}$

Q. A ship of mass $3\times {10}^{7}kg$ initially at rest is pulled by a force of $5\times {10}^{4}N$ through a distance of $3m$. Assume that the resistance due to water is negligible. The speed of the ship is

1. $1.5m/s$
2. $60m/s$
3. $0.1m/s$
4. $5m/s$

Q. A body under the action of a force
$\overrightarrow{F}=6\hat{i}-8\hat{j}+10\hat{k}$, acquires an acceleration of $1m/s^2$. The mass of this body must be

1. $10$ $kg$
2. $20$ $kg$
3. $10\sqrt{2}$ $kg$
4. $2\sqrt{10}$$kg$

Q. A mass of $100\text{g}$ strikes the wall with a speed of $5\text{m/s}$ at an angle as shown in the figure. It rebounds with the same speed. If the contact time is $2\times {10}^{-3}\text{s}$, then what is the force applied on the mass by the wall?

1. $500\sqrt{3}\text{N}$ to right
2. $500\sqrt{3}\text{N}$ to left
3. $250\sqrt{3}\text{N}$ to left
4. $250\sqrt{3}\text{N}$ to right

Q. A stone weighing $3kg$ falls from the top of a tower $100m$ high and buries itself $2m$ deep in sand. Find the time (in seconds) of penetration $(g=10m/s^2)$

1. $25\sqrt{5}$
2. $2\sqrt{5}$
3. $\frac{\sqrt{5}}{25}$
4. $\sqrt{5}$

Q. A circular disc reaches from top to bottom of an inclined plane of length $L$. When it slips down the plane, it takes 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 ______.

Q. The water is filled upto height of $12\text{m}$ in a tank having vertical sidewalls. A hole is made in one of the walls at a depth ${}^{\prime }{h}^{\prime }$ below the waterlevel.The value of $h$ for which the emerging stream of waterstrikes the ground at the maximum range is $\text{(in m})$.

Q. A $3\text{kg}$ steel ball strikes a wall with a speed of $10{\text{ms}}^{-1}$ at an angle of ${60}^{\circ }$ with the surface of the wall. The ball bounce off with the same speed and same angle. If the ball in contact with the wall for $0.25\text{s}$. The average force exerted by the wall on the ball is

1. $75\sqrt{3}\text{N}$
2. $30\sqrt{3}\text{N}$
3. $150\sqrt{3}\text{N}$
4. $60\sqrt{3}\text{N}$

Q. An elevator is accelerating upwards with an acceleration of $6{\text{m/s}}^2$. Inside it a person of mass $50\text{kg}$ is standing on a weighing machine having rough surface which is kept on an inclined plane having angle of inclination ${60}^{\circ }$. The reading of the weighing machine is -
$($Take $g=10{\text{m/s}}^2)$

1. $40\text{kg}$
2. $60\text{kg}$
3. $80\text{kg}$
4. $50\text{kg}$

Q.

A ball is thrown horizontally from a point 100 m above the ground with a speed of 20 m/s. Find

(a) The time it tskes to reach the ground,

(b) The horizontal distance it travels before reaching the ground,

(c) The velocity (direction and magnitude) with which it strikes the ground.

Q. Two blocks of masses $3\text{kg}$ and $2\text{kg}$ are tied to two ends of an inextensible string which passes over a frictionless pulley. The tension in the string between ceiling and the axle of pulley is

1. $24\text{N}$
2. $36\text{N}$
3. $48\text{N}$
4. $64\text{N}$

Q.

A 50 kg boy stands on a platform spring scale in a lift that is going down with a constant speed $3\text{m/s}$. If the lift is brought to rest by a constant deceleration in a distance of $9\text{m}$, what does the scale read (in Newtons) during this period? $(g=9.8{\text{m/s}}^2)$

Q.

A ball is thrown vertically upwards with a velocity $u$. The velocity with which it falls to the earth again is:

Q. A projectile is thrown with velocity $u$ making angle $\theta$ with the vertical. It just crosses the top of two poles each of height h after 1 sec and 3 sec respectively. The maximum height of projectile is

1. 9.8 m
2. 19.6 m
3. 4.9 m
4. 39.2 m

Q.

What is acceleration of free fall?

Q.

Calculate the tension in the string shown in figure. The pulley and the string are light and all surfaces are frictionless. Take g = 10 $m/s^2$.

Q.

What is the change in momentum of a car weighing 1500 kg when its speed increases from 36 km/h to 72 km/h uniformly?

Q. Two masses $m$ and $M$ are connected by a light string passing over a smooth pulley. When set free, $m$ moves up by $1.4\text{m}$ in $2\text{s}$. The ratio $\frac{m}{M}$ is $(g=9.8{\text{ms}}^{-2})$

1. $\frac{13}{15}$
2. $\frac{15}{13}$
3. $\frac{9}{7}$
4. $\frac{7}{9}$

Q. In the shown figure, two blocks one of mass $5\text{kg}$ and the other of mass $2\text{kg}$ are connected by light, inextensible strings and pulleys are light and frictionless. Choose the correct statement(s).

1. The acceleration of $5\text{kg}$ mass is $\frac{5\text{g}}{11}{\text{ms}}^{-2}$
2. The acceleration of $2\text{kg}$ mass is $\frac{5\text{g}}{11}{\text{ms}}^{-2}$
3. Tension in the string is $\frac{12\text{g}}{11}\text{N}$
4. Tension in the string is $\frac{10\text{g}}{11}\text{N}$

Q.

Assertion: The slope of momentum versus the time curve gives us the acceleration.

Reason: Acceleration is given by the rate of change of momentum.

1. If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.

2. If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion.

3. If Assertion is true but Reason is false.

4. If the Assertion and Reason both are false.

5. If Assertion is false but Reason is true.

Q. In a projectile motion let $v_x$ and $v_y$ be the horizontal and vertical components of velocity at any time $t$ and $x$ and $y$ be the displacements along horizontal and vertical from the point of projection at any time $t$. Then

1. $v_y-t$ graph is a straight line with negative slope and positive intercept.
2. $x-t$ graph is a straight line passing through origin.
3. $y-t$ graph is a straight line passing through origin.
4. $v_x-t$ graph is a straight line parallel to $t-$ axis.

Q. What is the maximum height of a projectile?

Q. A truck and a car are moving with equal velocity. If equal retarding force is applied to each of them on applying the brakes, both will stop after a certain distance. Then

1. Truck will cover less distance before rest
2. Car will cover less distance before rest
3. Both will cover equal distance
4. Cannot be determined

Q. A $0.2\text{kg}$ object at rest is subjected to a force $(0.3\hat{i}-0.4\hat{j})\text{N}$. What is the velocity of the object (in $m/s$) after $6\text{s}$

1. $(9\hat{i}-12\hat{j})$
2. $(8\hat{i}-16\hat{j})$
3. $(12\hat{i}-9\hat{j})$
4. $(16\hat{i}-8\hat{j})$

Q. Two persons of masses $m_1$ and $m_2$ are standing on a smooth surface facing each other holding a massless rope in their hands. If they pull each other with a force $F$, they meet each other

$(d$ is the initial distance between them$)$

1. after $\sqrt{\frac{m_1{m}_{2}d}{F(m_1+m_2)}}$ seconds at the mid point.
2. after $\sqrt{\frac{m_1{m}_{2}d}{F(m_1+m_2)}}$ seconds at the centre of mass
3. after $\sqrt{\frac{2m_1{m}_{2}d}{F(m_1+m_2)}}$ seconds at the mid point
4. after $\sqrt{\frac{2m_1{m}_{2}d}{F(m_1+m_2)}}$ seconds at the centre of mass

Q. A target is made of two plates, one of wood and the other of iron. The thickness of the wooden plate is $4\text{cm}$ and that of iron plate is $2cm$. A bullet fired goes through the wood first and then penetrates $1cm$ into the iron. A similar bullet fired with the same velocity from the opposite direction goes through the iron first and then penetrates $2\text{cm}$ into the wood. If $a_1$ and $a_2$ be the retardation offered to the bullet by the wood and iron plates respectively, then

1. $a_1=2a_2$
2. Data insufficient
3. $a_2=2a_1$
4. $a_1=a_2$