Laws of Motion

A projectile of mass 200 g is launched in a viscous medium at an angle $60^{\circ}$ with the horizontal, with an initial velocity of $270 \mathrm{~m} / \mathrm{s}$. It experiences a viscous drag force $\vec{F}=-c \vec{v}$ where the drag coe...

A particle of mass $m$ is moving in the $x y$-plane such that its velocity at a point $(x, y)$ is given as $\overrightarrow{\mathrm{v}}=\alpha(y \hat{x}+2 x \hat{y})$, where $\alpha$ is a non-zero constant. What is the force $\vec{F}$ actin...

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 the highest point of its trajectory splits into two equal parts. One part falls vertically ...

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 the highest point of its trajectory splits into two equal parts. One part falls vertically ...

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 tilted making an angle \(\theta\) from the horizontal as shown in
the figure below. The maxi...

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 move both the fingers slowly towards the center,
initially only the left finger slips with...

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 massless pulleys and strings. The accelerations of the blocks are a1, a2 and a3 as shown in ...

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 \(1.0\) \(Ns\) is applied to the block at time \(t=0\) so that it starts moving along the...

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 values of \(\theta\) are given in List I. The coefficient of friction between the block m1...

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 the below figure. The bead is released from near the top of the wire and it slides along t...

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. The coefficient of friction between the wall and the ladder is \(\mu\)1 and that between th...

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 the block through its centre of mass as shown in the figure. The block remains stationary ...

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 axis. The maximum tension that the string can bear is 324 N. The
maximum possible value o...

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 required to just push it up the inclined plane is 3 times the force required to just
prevent it ...

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 held
stationary by applying a force P parallel to the plane. The direction of force
pointing ...

A piece of wire is bent in the shape of a parabola y = kx2 (y-axis vertical) with a bead of mass m on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is no...

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 θ of this inclined plane from the horizontal plane is gradually
increased from $$0^\circ ...

STATEMENT 1 : It is easier to pull a heavy object than to push it on a level ground.
and
STATEMENT 2 : The magnitude of frictional force depends on the nature of the two surfaces in contact.

The speed of the block at point C, immediately before it leaves the second incline is

The speed of the block at point B immediately after it strikes the second incline is

A particle moves in the X - Y plane under the influence of a force such that its linear momentum is \(\overrightarrow p \left( t \right) = A\left[ {\widehat i\cos (kt) - \widehat j\sin (kt)} \right]\), where A and k are constants. The angle...

STATEMENT 1
A cloth covers a table. Some dishes are kept on it. The cloth can be pulled out without dislodging the dishes from the table.
STATEMENT 2
For every action there is an equal and opposite reaction.

Two particles of mass m each are tied at the ends of a light string of length 2a. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance 'a' form the centre P (as shown in...

A circular disc with a groove along its diameter is placed horizontally. A block of mass 1 kg is placed as shown. The coefficient of friction between the block and all surfaces of groove in contact is $\mu=\frac{2}{5}$. The disc has an acce...

Two blocks A and B of masses $2 m$ and $m$, respectively, are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in the figure. The magnitudes of acceleration of A and B, immediately...

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 be

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 wall is 0.5, the magnitude of the frictional force acting on the block is:

A uniform rod of length L and density \(\rho\) is being pulled along a smooth floor with a horizontal acceleration \(\alpha\) (see Fig.). The magnitude of the stress at the transverse cross-secion through the mid-point of the rod is _____...

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 \(+ \phi\). For an angular displacement \(\theta\) \(\left( {\left| \theta \right| < \phi } \right)\),...

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 in the string is greater than mg cos\(20^\circ\).

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 acceleration of the truck is 5 m/s2, the frictional force acting on the block is _________ new...

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 moves upwards with a speed

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 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 the block and the plane is 0.7. The frictional force on the block is

A rocket moves forward by pushing the surrounding air backwards.

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 resistance due to water is negligible, the speed of the ship is

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 at a distance \(l\) from the end where the force is applied?