$A$ balloon with mass $m$ is descending down with an acceleration $a$ (where $a < g$). How much mass should be removed from it so that it starts moving up with an acceleration $a$?

$A$ block of mass $5\,kg$ starting from rest is pulled up on a smooth inclined plane making an angle of $30^{\circ}$ with the horizontal with an effective acceleration of $1\,m/s^2$. The power delivered by the pulling force at $t = 10\,s$ from the start is $.....\,W$. [Use $g = 10\,m/s^2$] (calculate the nearest integer value).

$A$ particle is projected with a speed $v_0 = \sqrt{gR}$ at the bottom of a hemispherical bowl. The coefficient of friction between the particle and the hemispherical surface is $\mu = 0.5$. Then,the initial acceleration of the particle is:

$A$ block of mass $0.18 \ kg$ is attached to a spring of force-constant $2 \ N/m$. The coefficient of friction between the block and the floor is $0.1$. Initially,the block is at rest and the spring is un-stretched. An impulse is given to the block as shown in the figure. The block slides a distance of $0.06 \ m$ and comes to rest for the first time. The initial velocity of the block in $m/s$ is $v = N/10$. Then $N$ is:

$A$ 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

$A$ bird is sitting in a large closed cage which is placed on a spring balance. It records a weight of $25 \, N$. The bird (mass $m = 0.5 \, kg$) flies upward in the cage with an acceleration of $2 \, m/s^2$. The spring balance will now record a weight of ........ $N$.