$A$ balloon of mass $m$ is descending down with an acceleration $\frac{g}{2}$. How much mass should be removed from it so that it starts moving up with the same acceleration?

$A$ system consists of three masses $m_1, m_2$ and $m_3$ connected by a string passing over a pulley $P$. The mass $m_1$ hangs freely and $m_2$ and $m_3$ are on a rough horizontal table (the coefficient of friction $= \mu$). The pulley is frictionless and of negligible mass. The downward acceleration of mass $m_1$ is (Assume $m_1 = m_2 = m_3 = m$)

Masses of $10\, kg$ and $20\, kg$ are connected by a massless spring as shown in the figure. $A$ force of $200\, N$ acts on the $20\, kg$ mass. At the instant shown,the $10\, kg$ mass has an acceleration of $12\, m/s^2$. What is the acceleration of the $20\, kg$ mass in $m/s^2$?

Calculate the acceleration (in $m/s^{2}$) of the block and trolley system shown in the figure. The coefficient of kinetic friction between the trolley and the surface is $0.05$. (Given: $g = 10\; m/s^{2}$,mass of the string is negligible and no other friction exists).

$A$ disc of mass $100 \,g$ slides down from rest on an inclined plane of $30^{\circ}$ and comes to rest after travelling a distance of $1 \,m$ along the horizontal plane. If the coefficient of friction is $0.2$ for both inclined and horizontal planes, then the work done by the frictional force over the whole journey, approximately, is (Acceleration due to gravity, $g=10 \,ms^{-2}$) (in $\,J$)

$A$ vehicle without passengers is moving on a frictionless horizontal road with velocity $u$ and can be stopped in a distance $d$. Now,$40\%$ of its weight is added. If the retardation remains the same,what is the stopping distance at velocity $u$?