Laws of Motion

A batsman hits back a ball of mass 0.4 kg straight in the direction of the bowler without changing its initial speed of 15 ms$^{-1}$. The impulse imparted to the ball is ______ Ns.

A system to 10 balls each of mass 2 kg are connected via massless and unstretchable string. The system is allowed to slip over the edge of a smooth table as shown in figure. Tension on the string between the 7$^{\rm th}$ and 8$^{\rm th}$ ball is ______ N when 6$^{\rm th}$ ball just leaves the table.

A system of two blocks of masses $m=2$ kg and $M=8$ kg is placed on a smooth table as shown in figure. The coefficient of static friction between two blocks is 0.5. The maximum horizontal force F that can be applied to the block of mass M so that the blocks move together will be :

One end of a massless spring of spring constant $k$ and natural length $l_0$ is fixed while the other end is connected to a small object of mass $m$ lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity $\omega$ about an axis passing trough fixed end, then the elongation of the spring will be :

A mass of 10 kg is suspended vertically by a rope of length 5 m from the roof. A force of 30 N is applied at the middle point of rope in horizontal direction. The angle made by upper half of the rope with vertical is $\theta=\tan^{-1}\left(x\times10^{-1}\right)$. The value of $x$ is ______.

(Given, $g=10$ m/s$^2$)

A hanging mass M is connected to a four times bigger mass by using a string-pulley arrangement, as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by 2 Mg force. In this situation, tension in the string is $\frac x5$ Mg for x = ______. Neglect mass of the string and friction of the block (bigger mass) with ice slab.

(Given g = acceleration due to gravity)

A uniform disc with mass $M=4$ kg and radius $R=10$ cm is mounted on a fixed horizontal axle as shown in figure. A block with mass $m=2$ kg hangs from a massless cord that is wrapped around the rim of the disc. During the fall of the block, the cord does not slip and there is no friction at the axle. The tension in the cord is ______ N.

(Take $g=10$ ms$^{-2}$)

A block of metal weighing 2 kg is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of 1 kgs$^{-1}$ and at a speed of 10 ms$^{-1}$. Then, the initial acceleration of the block, in ms$^{-2}$, will be :

A block of mass 40 kg slides over a surface, when a mass of 4 kg is suspended through an inextensible massless string passing over frictionless pulley as shown below.

The coefficient of kinetic friction between the surface and block is 0.02. The acceleration of block is. (Given $g=10$ ms$^{-2}$.)

A block of mass M placed inside a box descends vertically with acceleration 'a'. The block exerts a force equal to one-fourth of its weight on the floor of the box. The value of 'a' will be

A 2 kg block is pushed against a vertical wall by applying a horizontal force of 50 N. The coefficient of static friction between the block and the wall is 0.5. A force F is also applied on the block vertically upward (as shown in figure). The maximum value of F applied, so that the block does not move upward, will be :

(Given : $g=10$ ms$^{-2}$)

Two bodies A and B of masses 5 kg and 8 kg are moving such that the momentum of body B is twice that of the body A. The ratio of their kinetic energies will be :

Four forces are acting at a point P in equilibrium as shown in figure. The ratio of force $F_1$ to $F_2$ is $1:x$ where $x=$ ______.

Two billiard balls of mass 0.05 kg each moving in opposite directions with 10 ms$^{-1}$ collide and rebound with the same speed. If the time duration of contact is $t=0.005$ s, then what is the force exerted on the ball due to each other ?

For a free body diagram shown in the figure, the four forces are applied in the '$x$' and '$y$' directions. What additional force must be applied and at what angle with positive x-axis so that the net acceleration of body is zero ?

Three masses M = 100 kg, $m_1$ = 10 kg and $m_2$ = 20 kg are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. A force F is applied on the system so that the mass $m_2$ moves upward with an acceleration of 2 ms$^{-2}$. The value of F is :

(Take $g=10$ ms$^{-2}$)

A monkey of mass 50 kg climbs on a rope which can withstand the tension (T) of 350 N. If monkey initially climbs down with an acceleration of 4 m/s$^2$ and then climbs up with an acceleration of 5 m/s$^2$. Choose the correct option ($g=10$ m/s$^2$).

A ball of mass 0.15 kg hits the wall with its initial speed of 12 ms$^{-1}$ and bounces back without changing its initial speed. If the force applied by the wall on the ball during the contact is 100 N, calculate the time duration of the contact of ball with the wall.

Two masses $M_1$ and $M_2$ are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass $M_2$ is twice that of $M_1$, the acceleration of the system is $a_1$. When the mass $M_2$ is thrice that of $M_1$, the acceleration of the system is $a_2$. The ratio $\dfrac{a_1}{a_2}$ will be :

A bag is gently dropped on a conveyor belt moving at a speed of 2 m/s. The coefficient of friction between the conveyor belt and bag is 0.4. Initially, the bag slips on the belt before it stops due to friction. The distance travelled by the bag on the belt during slipping motion, is : [Take g = 10 m/s$^{-2}$]