Find the accelerations $a_1, a_2$ and $a_3$ of the blocks if a $10\,N$ force $F$ is applied on the $3\,kg$ block as shown in the figure.

$A$ body of mass $3 \, kg$ hits a wall at an angle of $60^\circ$ with the wall and returns at the same angle. The speed of the body is $10 \, m/s$ and the impact time is $0.2 \, s$. Calculate the force exerted on the wall.

$A$ bird weighs $2 \ kg$ and is inside a closed cage of $1 \ kg$. If it starts flying,then what is the weight of the bird and cage assembly in $kg$?

$A$ spring is compressed between two blocks of masses $m_1$ and $m_2$ placed on a horizontal surface as shown in the figure. When the blocks are released,they have initial velocities $v_1$ and $v_2$ as shown. The blocks travel distances $x_1$ and $x_2$ respectively before coming to rest due to friction. The ratio $\left( \frac{x_1}{x_2} \right)$ is

$A$ gardener holds a hosepipe through which water is gushing out at a rate of $4\, kg\, s^{-1}$ with a speed of $2\, ms^{-1}$. The moment the speed of water is increased to $3\, ms^{-1}$,the gardener will experience a jerk of

Imagine the situation in which the given arrangement is placed inside a trolley that can move only in the horizontal direction,as shown in the figure. If the trolley is accelerated horizontally along the positive $x$-axis with $a_0$,then identify the correct statement$(s)$ related to the tension $T$ in the string.