$A$ heavy ball of mass $M$ is suspended from the ceiling of a car by a light string of mass $m$ $(m \ll M)$. When the car is at rest,the speed of transverse waves in the string is $60 \, ms^{-1}$. When the car has acceleration $a$,the wave-speed increases to $60.5 \, ms^{-1}$. The value of $a$,in terms of gravitational acceleration $g$,is closest to:

Three weights $A, B$ and $C$ are connected by strings as shown in the figure. The system moves over a frictionless pulley. The tension in the string connecting $A$ and $B$ is (where $g$ is acceleration due to gravity):

$A$ constant force $F = m_2g/2$ is applied on the block of mass $m_1$ as shown in the figure. The string and the pulley are light and the surface of the table is smooth. The acceleration of $m_1$ is

Two bodies $A$ and $B$ of masses $5 \, kg$ and $10 \, kg$ in contact with each other rest on a table against a rigid wall. The coefficient of friction between the bodies and the table is $0.15$. $A$ force of $200 \, N$ is applied horizontally to $A$. What are $(a)$ the reaction of the partition $(b)$ the action-reaction forces between $A$ and $B$? What happens when the wall is removed? Does the answer to $(b)$ change,when the bodies are in motion? Ignore the difference between $\mu_{s}$ and $\mu_{k}$.

Consider the following statements $A$ and $B$ and identify the correct answer given below:
$(A)$ $A$ body initially at rest is acted upon by a constant force. The rate of change of its kinetic energy varies linearly with time.
$(B)$ When a body is at rest, it must be in equilibrium.

Two blocks ($P$ and $Q$) with masses $2 \text{ kg}$ and $1.5 \text{ kg}$ respectively are joined by a massless thread. These blocks are mounted on a frictionless pulley which is fixed on the edge of a cube $(S)$, as shown in the figure. Block $P$ is positioned on the top surface which has no friction, and block $Q$ is in contact with the side surface, which has a coefficient of friction $\mu$. The cube $(S)$ moves towards the right with an acceleration of $g/2$, where $g$ is the gravitational acceleration. During this movement, the blocks $P$ and $Q$ remain stationary relative to the cube. The value of $\mu$ is . . . . . . . (Take $g = 10 \text{ m/s}^2$)