Laws of Motion

A ball of mass 0.15 kg hits the wall with its initial speed of 12 ms^-1and 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 during of the contact of ball with the wall.

Two masses A and B, each of mass M are fixed together by a massless spring. A force acts on the mass B as shown in figure. If the mass A starts moving away from mass B with acceleration ‘a’, then the acceleration of mass B will be

Blocks of masses $m,2m$ and $8m$ are arranged in a line on a frictionless floor. Another block of mass $m$ , moving with speed $v$ along the same line (see figure) collides with mass $m$ in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass $8\mathrm{m}$ starts moving the total energy loss is $\mathrm{p}\mathrm{\%}$ of the original energy. Value of ' $p$ ' is close to:

A uniform metal chain of mass m length ‘L’ passes over a massless and frictionless pulley. It is released from rest with a part of its length $\text{'}\mathcal{l}\text{'}$ is hanging on one side and rest of its length $\text{'}L-\mathcal{l}\text{'}$ is hanging on the other side of the pully. At a certain point of time, when $\mathcal{l}=\frac{L}{x},$ the acceleration of the chain is $\frac{g}{2}.$ The value of x is__________.

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 $\frac{x}{5}Mg$ <!-- [if gte mso 9]><xml> </xml><![endif]--> for x_________. Neglect mass of the string and fiction of the block (bigger mass) with ice slab.

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration (a) is varying with time t as a = k² rt², where k is a constant. The power delivered to the particle by the force acting on it is given as

The time period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination , is given by:

A smooth circular groove has a smooth vertical wall as shown in figure. A block of mass m moves against the wall with a speed v. Which of the following curve represents the correct relation between the normal reaction on the block by the wall (N) and speed of the block (v)?

A small ball of mass $m$ is thrown upward with velocity $u$ from the ground. The ball experiences a resistive force ${\mathrm{m}\mathrm{k}\mathrm{v}}^2$ where $v$  is it speed. The maximum height attained by the ball is:
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A mass of 10kg is suspended vertically by a rope of length 5m 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 q = tan^-1 (x × 10^-1). The value of x is…………….

(Given, g = 10 m/s²)