Equations of Motion

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 plates is $2\text{cm}$. A bullet fired goes through the wood first and then penetrates $1\text{cm}$ 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. $a_2=2a_1$
3. $a_1=a_2$
4. $a_1=3a_2$

Q. A body of mass $1kg$ is traveling with a velocity of $3m/s$ accelerates uniformly with $8m/s^2$ to travel for $2s$. Find its final momentum

1. $19Ns$
2. $6Ns$
3. $12Ns$
4. $20Ns$

Q. The figure shows an accelerometer, a device for measuring the horizontal acceleration of cars and airplanes. A ball is free to roll on a parabolic track described by the equation $y=x^2$, where both $x$ and $y$ are in meters. A scale along the bottom is used to measure the ball's horizontal position $x$. The mass of ball is $\frac{4}{70}\text{kg}$. The accelerometer is free to move along the horizontal.

What is the magnitude of normal reaction (in $\text{N}$) by track on ball if ball remains at rest at $x=2\sqrt{3}$.
(Given that, $\sin \theta =\frac{4\sqrt{3}}{7}$), where $\theta$ is the angle made by the tangent with the horizontal at this point. Take $g=10m{s}^{-2}$

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 force of $5kg-wt$ is acting on a body of mass $5kg$ kept on a smooth horizontal surface at rest. If it acts for $10$ seconds at an angle of ${60}^{\circ }$ with the horizontal, find the distance travelled by the body. (Take $g=10m/s^2)$

1. $100m$
2. $150m$
3. $200m$
4. $250m$

Q. A body of mass $1\text{kg}$ is subjected to a force of $20\text{N}$ for $10$ seconds after which the force ceases to act. What distance would it travel in the next $10$ seconds?

1. $2\text{km}$
2. $3\text{km}$
3. $4\text{km}$
4. $5\text{km}$

Q. A body of mass $5\text{kg}$ is moving along a straight line with a velocity of $2{\text{ms}}^{-1}$. A variable force $F$ started acting on it for a time period of $0.5s$ as shown in force - time curve. The final velocity of the block is

1. $2{\text{ms}}^{-1}$
2. $2.2{\text{ms}}^{-1}$
3. $2.5{\text{ms}}^{-1}$
4. $2.7{\text{ms}}^{-1}$

Q. A person A moving in a car with a speed of $10\text{m/s}$ drops a stone of mass $10\text{gm}$. A person B on the ground measures the momentum of the stone 1 sec after the stone is dropped. Find the momentum ($\text{kg m/s}$) of the stone as measured by B. (Take $g=10{\text{m/s}}^2$)

1. $0.707$
2. $0.14$
3. $1.4$
4. $7.07$

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. 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. 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. A body of mass $1kg$, traveling with a velocity of $3m/s$, accelerates uniformly to acquire a velocity of $8m/s$ in $2s$. Find the force acting on the body.

1. $2N$
2. $2.5N$
3. $4N$
4. $5N$

Q. A force acts for 10 sec on a body of mass $100\text{kg}$ after which it ceases. If the body travels $160\text{m}$ in the next 8 sec, find the magnitude of the force.

1. $100\text{N}$
2. $200\text{N}$
3. $300\text{N}$
4. $400\text{N}$

Q. A force of $5\text{kg – wt}$ is acting on a body of mass $5\text{kg}$ kept on a smooth horizontal surface at rest. If it acts for $10$ seconds at an angle of ${60}^{\circ }$ with the horizontal, find the distance travelled by it along the surface (Take $g=10{\text{m/s}}^2$)

1. $100\text{m}$
2. $150\text{m}$
3. $200\text{m}$
4. $250\text{m}$

Q. A force of $5\text{kg – wt}$ is acting on a body of mass $5\text{kg}$ kept on a smooth horizontal surface at rest. If it acts for $10$ seconds at an angle of ${60}^{\circ }$ with the horizontal, find the distance travelled by it along the surface (Take $g=10{\text{m/s}}^2$)

1. $100\text{m}$
2. $150\text{m}$
3. $200\text{m}$
4. $250\text{m}$

Q. A body of mass $5\text{kg}$ is moving along a straight line with a velocity of $2{\text{ms}}^{-1}$. A variable force $F$ started acting on it for a time period of $0.5s$ as shown in force - time curve. The final velocity of the block is

1. $2{\text{ms}}^{-1}$
2. $2.2{\text{ms}}^{-1}$
3. $2.5{\text{ms}}^{-1}$
4. $2.7{\text{ms}}^{-1}$

Q. A train has each compartment of mass $m$ is accelerating uniformly. At the instant they cross a certain mile maker, the velocity of the engine is $v_1$ and the velocity of the last compartment is $v_2$. Find the momentum of the compartment in the middle when it passes the same mile marker assuming that the compartments are of point sizes.

1. $m\sqrt{\frac{V_1^2-V_2^2}{2}}$
2. $m\sqrt{\frac{V_1^2{V}_2^2}{2}}$
3. $m\times (\frac{V_1^2-V_2^2}{2}$)
4. $m\times (\frac{V_1^2+V_2^2}{2}$)