Laws of motion practice · Mixed difficulty

A 500 kg horse pulls a cart of mass 1500 kg along a level road with an acceleration of $1\;m{s^{ - 2}}$. If the coefficient of sliding friction is 0.2, then the force exerted by the horse in forward direction is

Pendulum after some time becomes slow in motion and finally stops due to

Statement-I: A man in a closed cabin falling freely does not experience gravity
Statement-II: Inertial and gravitational mass have equivalence

When a body is stationary

A body is moving with a speed of $1 \mathrm{~ms}^{-1}$ and a force $\mathrm{F}$ is needed to stop it in a distance $x$. If the speed of the body is $3 \mathrm{~ms}^{-1}$, the force needed to stop it in the same distance $\mathrm{x}$ will be

A rocket is fired with a speed $u=3 \sqrt{g R}$ from the earth surface. What will be its speed at interstellar space?

Select the wrong statement(s) from the following.
I. Newton's laws of motion hold good for both inertial and non-inertial frames

II. During explosion, linear momentum is conserved
III. Force of friction is zero when no driving force is applied

A lorry starting from rest moving with acceleration $2 {~m} / {s}^2$, has a trolley $4.5 {~m}$ long. A box is placed at $4.5 {~m}$ from the open end and coefficient of friction between box and lorry is 0.02 . The distance covered by the lorry by the time the box falls off the trolley is $\left({g}=10 {~m} / {s}^2\right)$

Assertion (A) : Speed of a particle moving in a circle varies with time as, $v=(4 t-12)$. Such type of circular motion is not possible.

Reason (R) : Speed cannot change linearly with time.

An initially stationary device lying on a frictionless floor explodes into two pieces and slides across the floor. One piece is moving in positive $x$-direction, then other piece is moving in

Inside a horizontally moving box, an experimenter finds that when an object is placed on a smooth horizontal table and is released, it moves with an acceleration of $10 \mathrm{~ms}^{-2}$. In this box, if 1-kg body is suspended with a light string, the tension in the string in equilibrium position. (w.r.t. experimenter) will be (take $g=10 \mathrm{~ms}^{-2}$ )

A disc revolves in a horizontal plane at a steady rate of 3 rad/s. A coin will remain on the disc if kept at a distance of 20 cm from the axis of rotation. The coefficient of friction ( $g = 10\,m/{s^2}$) is:

Two guns A and B can fire bullets at speeds 1 km/s and 2 km/s, respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets on the ground fired by the two guns is

Rocket engines lift a rocket from the earth surface because hot gas with high velocity

A nucleus of mass $M$ breaks into 3 nuclei with a mass defect of $\Delta m$. Find the speed of each daughter nuclei if they have equal mass.

A body of mass $m$ moving with a constant velocity $V$ hits another body of the mass $m$ moving with same velocity $V$ but in the opposite direction, and sticks to it. The velocity of the compound body after collision is :

A machine gun fires a bullet of mass 40 grams with a velocity $1200\,\,m{s^{ - 1}}$ . The man holding it can
exert a maximum force of 144 N on the gun. The number of bullets he can fire per second at the most is

In case of uniform circular motion which of the following physical quantity do not remain constant

Assertion: A rocket in flight is an illustration of the application of the principle of conservation of linear momentum of a system of varying mass.

Reason: The linear momentum of the exhaust gases becomes irrelevant, as these gases no longer remain a part of the rocket.

Which motion does not require force to maintain it?

Assertion (A) A particle of mass $M$ at rest decay into two particles of masses $m_1$ and $m_2$, having non-zero velocities will have ratio of de-Broglie wavelengths unity.

Reason (R) Here we cannot apply conservation of linear momentum.

Assertion: The words 'action' and 'reaction' in the third law of motion stand for simultaneous mutual forces between a pair of objects.
Reason: In this context action always precede or cause reaction.

A thief stole a box full of valuable articles of weight w and while carrying it on his head jumped down from a wall of height $h$ from the ground. Before he reaches the ground, he experienced a load

A hammer of mass $10 \mathrm{~kg}$ moving with a speed of $5 \mathrm{~m} / \mathrm{s}$ strikes the head of a nail driving it $30 \mathrm{~cm}$ into the wall. Find the impulse imparted to the nail.

A body of mass 60 kg is pushed with just enough force to start it moving on a rough surface with ${\mu _s} = 0.5$ and ${\mu _k} = 0.4$ and the force continues to act afterwards. The acceleration of the body is $\left( {\mathrm{in}\,m/{{\sec }^2}} \right)$

A rocket motor consumes $100 \mathrm{~kg}$ of fuel per second, exhausting it with a speed of $5 \times 10^3 \mathrm{~ms}^{-1}$. What force is exerted on the rocket?

Assertion: A table cloth can be pulled from a table without dislodging the table.
Reason: For a moving object, if its speed changes, its velocity must change and it must have some acceleration.

Three weights $\mathrm{W}, 2 \mathrm{~W}$ and $3 \mathrm{~W}$ are connected to identical springs suspended from rigid horizontal rod. The assembly of the rod and the weights fall freely. The positions of the weights from the rod are such that

Select the incorrect statement(s) from the following.
I. Limiting friction is always greater than the kinetic friction
II. Limiting friction is always less than the static friction
III. Coefficient of static fiction is always greater than the coefficient of kinetic fiction

A bullet of mass $20 {~g}$ moving with a speed of $100 {~m} {~s}^{-1}$ enters a heavy wooden block and stops after a distance of $50 {~cm}$. The average resistive force exerted by the block on the bullet is