Laws of motion practice · Mixed difficulty

Statement-I: If the force varies with time in a complicated way then the net force is measured by the total change in momentum of the body.
Statement-II: Change in momentum and impulsive force are numerically equal.

One end of a string of length $l$ is connected to a particle of mass m and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed v, the net force on the particle (directed towards the centre) is

The mass of a body measured by a physical balance in the lift at rest is found to be m. If the lift is going up with an acceleration a, its mass will be measured as

Three forces are acting on a body to make it in equilibrium, which set can not do it?

A ball is projected from ground with initial momentum p at an angle $\theta$. What is the magnitude of net change in linear momentum when it reaches at maximum height of journey?

$n$ balls each of mass impinge elastically (bounce back with same speed) in each second on a surface with velocity $u$. The average force experienced by the surface will be

A ball moves in a frictionless inclined table without slipping. The work done by the table surface on the ball is

A block of mass $100 {~kg}$ slides over a distance of $10 {~m}$ on a horizontal surface. If the co-efficient of friction between the surface is 0.4, then the work done against friction (in $J$) is:

Formula for true force is

An object flying in the air with velocity $(20 \hat{i}+25 \hat{j}-12 \hat{k})$ suddenly breaks into two pieces whose masses are in the ratio of $1: 5.$ The smaller mass flies off with a velocity $(100 \hat{i}+35 \hat{j}+8 \hat{k}).$ The velocity of the larger piece will be:

An object is placed on the surface of a smooth inclined plane of inclination $\theta$. It takes time $t$ to reach the bottom of the inclined plane. If the same object is allowed to slide down rough inclined plane of same inclination $\theta$, it takes time nt to reach the bottom where $\mathrm{n}$ is a number greater than 1 . The coefficient of friction $\mu$ is given by

A body of mass M is kept on a rough horizontal surface (friction coefficient $\mu$). A person is trying to pull the body by applying a horizontal force but the body is not moving. The force by the surface on the body is F, where

Which of the following statement (s) is/are incorrect?

A particle of mass $m$ travelling along $x$-axis with speed $v_0$ shoots out $1 / 3^{\text {rd}}$ of its mass with a speed $2 v_0$ along $y$-axis. The velocity of remaining piece is:

A ball of mass $m$ moves with speed $v$ and it strikes normally with a wall and reflected back normally, if its time of contact with wall is $t$ then find force exerted by ball on wall

There are different types of inertia called
I. Inertia of rest.
II. Inertia of motion.
III. Inertia of direction.
IV. Inertia of shape.
Choose the correct option.

A person sitting in an open car moving at constant velocity throws a ball vertically up into air. The ball falls

Three blocks A, B and C of masses $3 \mathrm{~kg}, 2 \mathrm{~kg}$ and $1 \mathrm{~kg}$ respectively connected by two ideal strings are present on a smooth horizontal surface. An external horizontal force of $18 \mathrm{~N}$ acts on the block A to pull the system. Find the difference in the tensions in strings connecting A $\&$ B and, B $\&$ C (in Newton).

A body of mass 10 kg is moving with a uniform velocity $100\,cm{s^{ - 1}}.$ The force required to stop the vehicle in 10 s is

Which of the following is NOT a fundamental force in nature?

A car is moving with a uniform speed on a level road. Inside the car there is a balloon filled with helium and attached to a piece of string tied to the floor. The string is observed to be vertical. The car now takes a left turn maintaining the speed on the level road. The balloon in the car will (Here the car is supposed to be air tight)

Maximum speed of car for safe turning on horizontal road is

A stationary bomb explodes into two parts of masses 3kg and 1kg. The total KE of the two parts after explosion is 2400 J. The KE of smaller part is

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

Assertion(A): Even though net external force on a body is zero, momentum need not to conserved.

Reason(R): The internal interaction between particles of a body cancels out momentum of each other.

Assertion: If the magnitude of net external force on a body is zero, its acceleration will be zero.
Reason: The given statement is the also a form of Newton’s second law of motion.

Impulse equals

STATEMENT-1 : A block of mass $m$ starts moving on a rough horizontal surface with a velocity $v$. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of $30^{\circ}$ with the horizontal and the same block is made to go up on the surface with the same initial velocity $v$. The decrease in the mechanical energy in the second situation is smaller than that in the first situation.

STATEMENT-2 : The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.

A block of mass 2 kg rests on a rough inclined plane making an angle of $30^\circ$ with the horizontal. If ${\mu _S} = 0.6$, what is the frictional force on the block?

In an explosion a body breaks up into two pieces of unequal masses. In this