$A$ 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?

Three blocks with masses $m$,$2m$,and $3m$ are connected by strings,as shown in the figure. After an upward force $F$ is applied on block $m$,the masses move upward at a constant speed $v$. What is the net force on the block of mass $2m$? ($g$ is the acceleration due to gravity)

$A$ block of mass $2M$ is attached to a massless spring with spring-constant $k$. This block is connected to two other blocks of masses $M$ and $2M$ using two massless pulleys and strings. The accelerations of the blocks are $a_1, a_2$ and $a_3$ as shown in the figure. The system is released from rest with the spring in its unstretched state. The maximum extension of the spring is $x_0$. Which of the following option$(s)$ is/are correct? [$g$ is the acceleration due to gravity. Neglect friction]

$A$ block of mass $5\, kg$ is $(i)$ pushed in case $(A)$ and $(ii)$ pulled in case $(B)$,by a force $F = 20\, N$,making an angle of $30^o$ with the horizontal,as shown in the figures. The coefficient of friction between the block and floor is $\mu = 0.2$. The difference between the accelerations of the block,in case $(B)$ and case $(A)$ will be ........ $ms^{-2}$ .$(g = 10\, ms^{-2})$

Given $m_1 = 4m_2$. The acceleration of $m_1$ is $a$. Find the velocity of $m_2$ at $t = 0.4 \, s$ in $cm/s$.

$A$ pebble of mass $0.05 \, kg$ is thrown vertically upwards. Give the direction and magnitude of the net force on the pebble,$(a)$ during its upward motion,$(b)$ during its downward motion,$(c)$ at the highest point where it is momentarily at rest. Do your answers change if the pebble was thrown at an angle of $45^{\circ}$ with the horizontal direction? Ignore air resistance.