A balloon has mass of $10 \mathrm{g}$ in air. The air escapes from the balloon at a uniform rate with velocity $4.5 \mathrm{cm} {\mathrm{s}}^{-1}$. If the balloon shrinks in $5 \mathrm{s}$ completely. Then, the average force acting on that balloon will be (in dyne).

A uniform metal chain of mass $m$ and length $L$ passes over a massless and frictionless pulley. It is released from rest with a part of its length $l$ is hanging on one side and rest of its length $L-l$  is hanging on the other side of the pulley. At a certain point of time, when $l=\frac{L}{x}$, the acceleration of the chain is $\frac{g}{2}$. The value of $x$ is _____.

A smooth circular groove has a smooth vertical wall as shown in figure. A block of mass $m$ moves against the wall with a speed $v$. Which of the following curve represents the correct relation between the normal reaction on the block by the wall $\left(N\right)$ and speed of the block $\left(v\right)$?

Two bodies of masses $m_1=5 \mathrm{kg}$ and $m_2=3 \mathrm{kg}$ are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined plane on the body of mass $m_1$ will be : [Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$]

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As per given figure, a weightless pulley $P$ is attached on a double inclined frictionless surface. The tension in the string (massless) will be (if $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A spherical body of mass $2 \mathrm{kg}$ starting from rest acquires a kinetic energy of $10000 \mathrm{J}$ at the end of $5^{\text{th }}$ second. The force acted on the body is _____ $\mathrm{N}$.