Laws of Motion

There are two inclined surfaces of equal length (\(L\)) and same angle of inclination \(45^\circ\) with the horizontal. One of them is rough and the other is perfectly smooth. A given body takes 2 times as much time to slide down on rough surface than on the smooth surface. The coefficient of kinetic friction (\(\mu_k\)) between the object and the rough surface is close to

A ball of mass 0.5 kg is dropped from a height of 40 m. The ball hits the ground and rises to a height of 10 m. The impulse imparted to the ball during its collision with the ground is (Take g = 9.8 m/s\(^2\))

A bob is whirled in a horizontal plane by means of a string with an initial speed of \(\omega\) rpm. The tension in the string is \(T\). If speed becomes \(2\omega\) while keeping the same radius, the tension in the string becomes :

A horizontal force 10 \(N\) is applied to a block \(A\) as shown in figure. The mass of blocks \(A\) and \(B\) are 2 kg and 3 kg, respectively. The blocks slide over a frictionless surface. The force exerted by block \(A\) on block \(B\) is :

A football player is moving southward and suddenly turns eastward with the same speed to avoid an opponent. The force that acts on the player while turning is :

Calculate the maximum acceleration of a moving car so that a body lying on the floor of the car remains stationary. The coefficient of static friction between the body and the floor is 0.15 (\(g=10\,\mathrm{m\,s^{-2}}\)).

A shell of mass m is at rest initially. It explodes into three fragments having mass in the ratio 2 : 2 : 1. If the fragments having equal mass fly off along mutually perpendicular directions with speed \(v\), the speed of the third (lighter) fragment is :

A ball of mass 0.15 kg is dropped from a height 10 m, strikes the ground and rebounds to the same height. The magnitude of impulse imparted to the ball is (g = 10 m/s\(^2\)) nearly :

Two bodies of mass 4 kg and 6 kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity (g) is :

A particle moving with velocity \(\vec{V}\) is acted by three forces shown by the vector triangle PQR. The velocity of the particle will :

A block of mass 10 kg is in contact against the inner wall of a hollow cylindrical drum of radius 1 m. The coefficient of friction between the block and the inner wall of the cylinder is 0.1. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be : (\(g = 10\) m/s\(^2\))

A block of mass m is placed on a smooth inclined wedge ABC of inclination \(\theta\) as shown in the figure. The wedge is given an acceleration 'a' towards the right. The relation between a and \(\theta\) for the block to remain stationary on the wedge is

Which one of the following statements is incorrect ?

One end of string of length \(l\) is connected to a particle of mass 'm' and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed 'v', the net force on the particle (directed towards center) will be (T represents the tension in the string)

Two blocks A and B of masses 3m and m respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of A and B immediately after the string is cut, are respectively :

A car is negotiating a curved road of radius R. The road is banked at an angle \(\theta\). The coefficient of friction between the tyres of the car and the road is \(\mu_s\). The maximum safe velocity on this road is :

A rigid ball of mass \(m\) strikes a rigid wall at 60° and gets reflected without loss of speed as shown in the figure below. The value of impulse imparted by the wall on the ball will be