$A$ 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?

Among the forces in nature,friction can be classified into

$A$ point particle of mass $m$ moves along the uniformly rough track $PQR$ as shown in the figure. The coefficient of friction between the particle and the rough track equals $\mu$. The particle is released from rest from the point $P$ and it comes to rest at a point $R$. The energies lost by the particle over the parts $PQ$ and $QR$ of the track are equal to each other,and no energy is lost when the particle changes direction from $PQ$ to $QR$. The values of the coefficient of friction $\mu$ and the distance $x (= QR)$ are,respectively,close to

$A$ block of mass $m$ is placed on a smooth horizontal surface. $A$ force making an angle $\theta$ with the horizontal starts acting on the block. The magnitude of the force is constant but its direction with the horizontal changes as $\theta = a + bs$,where $a$ and $b$ are constants and $s$ is the distance covered by the block. If $|F| = 2mb$,find the velocity of the block as a function of the angle $\theta$.

$A$ cylinder is placed on a rough plank,which in turn is placed on a smooth surface. The plank is pulled with a constant force $F$. Indicate the correct direction of the friction force acting on the cylinder.

$A$ car of mass $500\, kg$ is driven with acceleration $1\, m/s^2$ along a straight level road against a constant external resistance of $1000\, N$. When the velocity is $5\, m/s$,the rate at which the engine is working is .............. $kW$.