## Numerical

A projectile is thrown from a point O on the ground at an angle 45$$^\circ$$ from the vertical and with a speed 5$$\sqrt 2 $$ m/s. The projectile at t...

A projectile is thrown from a point O on the ground at an angle 45$$^\circ$$ from the vertical and with a speed 5$$\sqrt 2 $$ m/s. The projectile at t...

Put a uniform meter scale horizontally on your extended index fingers with the left one at 0.00 cm
and the right one at 90.00 cm. When you attempt to ...

A solid horizontal surface is covered with a thin layer of oil. A rectangular block of mass $$m=0.4$$ $$kg$$ is at rest on this surface. An impulse of...

A block is moving on an inclined plane making an angle $$45^\circ $$ with the horizontal and the coefficient of friction is $$\mu $$. The force requir...

## MCQ (Single Correct Answer)

A football of radius R is kept on a hole of radius r (r < R) made on a plank kept horizontally. One
end of the plank is now lifted so that it gets ...

A wire, which passes through the hole in a small bead, is bent in the form of quarter of a circle. The wire is fixed vertically on ground as shown in ...

A block of mass m1 = 1 kg another mass m2 = 2 kg, are placed together (see figure) on an inclined plane with angle of inclination $$\theta$$. Various ...

A ball of mass (m) 0.5 kg is attached to the end of a string having length (L) 0.5 m. The ball is rotated on a horizontal circular path about vertical...

A block of mass m is on an inclined plane of angle θ. The coefficient of
friction between the block and the plane is μ and tan θ > μ. The block is ...

A block of base 10 cm × 10 cm and height 15 cm is kept on an inclined plane. The coefficient of friction
between them is $$\sqrt 3 $$. The inclination...

A particle moves in the X - Y plane under the influence of a force such that its linear momentum is $$\overrightarrow p \left( t \right) = A\left[ {\w...

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle $$\theta $$ should b...

A block of mass 0.1 is held against a wall applying a horizontal force of 5 N on the block. If the coefficient of friction between the block and the w...

A block of mass 2 kg rests on a rough inclined plane making an angle of $$30^\circ $$ with the horizontal. The coefficient of static friction between ...

A ship of mass 3 $$ \times $$ 107 kg initially at rest, is pulled by a force of 5 $$ \times $$ 104 N through a distance of 3 m. Assuming that the resi...

## MCQ (More than One Correct Answer)

A block of mass 2M is attached to a massless spring with spring-constant k.This block is connected to two other blocks of masses M and 2M using two ma...

In the figure, a ladder of mass m is shown leaning against a wall. It is in static equilibrium making an angle $$\theta$$ with the horizontal floor. T...

A small block of mass 0.1 kg lies on a fixed inclined plane PQ which makes an angle $$\theta$$ with the horizontal. A horizontal force of 1 N acts on ...

A reference frame attached to the earth

A simple pendulum of length L and mass (bob) M is oscillating in a plane about a vertical line between angular limit $$ - \phi $$ and $$ + \phi $$. Fo...

In the arrangement shown in Fig. the ends P and Q of an unstretchable string move downwards with uniform speed U. Pulleys A and B are fixed.
Mass M mo...

## Fill in the Blanks

A uniform rod of length L and density $$\rho $$ is being pulled along a smooth floor with a horizontal acceleration $$\alpha $$ (see Fig.). The magnit...

A block of mass 1 kg lies on a horizontal surface in a truck. The coefficient of static friction between the block and the surface is 0.6. If the acce...

## True or False

A simple pendulum with a bob of mass m swings with an angular amplitude of $$40^\circ $$. When its angular displacement is $$20^\circ $$, the tension ...

When a person walks on a rough surface, the frictional force exerted by the surface on the person is opposite to the direction of his motion.

A rocket moves forward by pushing the surrounding air backwards.

## Subjective

A horizontal uniform rope of length L, resting on a frictionless horizontal surface, is pulled at one end by force F. What is the tension in the rope ...