## Numerical

A projectile is fired from horizontal ground with speed $v$ and projection angle $\theta$. When the acceleration due to gravity is $g$, the range of t...

A ball is thrown from ground at an angle $$\theta $$ with horizontal and with an initial speed u0. For the resulting projectile motion, the magnitude ...

A ball is projected from the ground at an angle of $${45^o}$$ with the horizontal surface. It reaches a maximum height of $$120$$ $$m$$ and returns to...

Airplanes A and B are flying with constant velocity in the same vertical plane at angles $$30^\circ $$ and $$60^\circ $$ with
respect to the horizonta...

A rocket is moving in a gravity free space with a constant
acceleration of 2 ms–2 along + x direction (see figure). The
length of a chamber inside the...

A train is moving along a straight line with a constant acceleration 'a'. A boy standing in the train throws a
ball forward with a speed of 10 m/s, at...

## MCQ (More than One Correct Answer)

Starting at time t = 0 from the origin with speed 1 ms-1, a particle follows a two-dimensional trajectory in the x-y plane so that its coordinates are...

The coordinates of a particle moving in a plane are given by x(t) = a cos(pt) and y(t) = b sin(pt) where a, b (< a) and p are positive constants of...

A particle of mass m moves on the x-axis as follows: it starts from rest at t = 0 from the point x = 0, and come to rest at t = 1 at the point x = 1. ...

A particle is moving eastwards with a velocity of 5 m/s. In 10s the velocity changes to 5 m/s northwards. The average acceleration in this time is

## MCQ (Single Correct Answer)

Consider an expanding sphere of instantaneous radius R whose total mass remains constant. The expansion is such that the instantaneous density $$\rho ...

Three vectors $$\overrightarrow P ,\overrightarrow Q $$ and $$\overrightarrow R $$ are shown in the figure. Let $$S$$ be any point on the vector $$\o...

STATEMENT-1: For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the
opposite direction to the...

A body starts from rest at time t = 0, the acceleration time graph is
shown in the figure. The maximum velocity attained by the body
will be
...

A particle starts sliding down a frictionless inclined plane. If Sn is the distance traveled by it from time t = n - 1 sec to t = n sec, the ratio Sn ...

A boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the r...

A river is flowing from west to east at a speed of 5 meters per minute. A man on the south bank of the river, capable of swimming at 10 meters per min...

## Subjective

Two guns, situated on the top of a hill of height 10 m, fire one shot each with the same speed $$5\sqrt 3 $$ m s-1 at some interval of time. One gun f...

The dispalcement x of particle moving in one direction, under the action of a constant force is related to the time t by the equation $$t = \sqrt x +...

Answer the following giving reason in brief:
Is the time variation of position, shown in the figure observed in nature?
...

A car accelerates from rest at a constant rate $$\alpha $$ for some time after which it decelerates at a constant rate $$\beta $$ to come to rest. If ...

## True or False

Two identical trains are moving on rails along the equator on the earth in opposite directions with the same speed. They will exert the same pressure ...

A projectile fired from the ground follows a parabolic path. The speed of the projectile is minimum at the top of its path.

Two balls of different masses are thrown vertically upwards with the same speed. They pass through the point of projection in their downward motion wi...

## Fill in the Blanks

Four person K, L, M, N are initially at the four corners of a square of side d. Each person now moves with a uniform speed v in such a way that K alwa...

A particle moves in a circle of radius R. In half the period of revolution its displacement is ________ and distance covered is _________.