Laws of Motion

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 $\frac{x}{5}Mg$  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:

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)

One end of a massless spring of spring constant k and natural length ${\mathcal{l}}_0$  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 through fixed end, then the elongation of the spring will be