In the figure,the mass of a ball is $\frac{9}{5}$ times the mass of the rod. The length of the rod is $1 \, m$. The initial level of the ball is the same as the lower end of the rod. Find the time taken by the ball to reach the upper end of the rod. (in $s$)

Two blocks $A$ and $B$ of masses $1.5 \ kg$ and $0.5 \ kg$ respectively are connected by a massless inextensible string passing over a frictionless pulley as shown in the figure. Block $A$ is lifted until block $B$ touches the ground and then block $A$ is released. The initial height of block $A$ is $80 \ cm$ when block $B$ just touches the ground. The maximum height reached by block $B$ from the ground after the block $A$ falls on the ground is (in $cm$)

$A$ bob of mass $m$ is hanging from a pulley inside a car by a string. The other end of the string is held by a person standing in the car. The car is moving with a constant horizontal acceleration '$a$' as shown in the figure. The other end of the string is pulled with a constant acceleration '$a$' vertically downward. The tension in the string is equal to-

Two masses $8\; kg$ and $12\; kg$ are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses and the tension in the string when the masses are released.

$A$ mass of $10 \; kg$ is suspended by a rope of length $4 \; m$ from the ceiling. $A$ force $F$ is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of $45^{\circ}$ with the vertical. Then $F$ equals ........... $N$ (Take $g = 10 \; ms^{-2}$ and the rope to be massless).

$A$ block of mass $1\,kg$ is suspended by a string of mass $1\,kg$ and length $1\,m$ as shown in the figure. $(g = 10\,m/s^2)$. Calculate the tension (in $N$) in the string at its lowest point.