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 _____ $\mathrm{N}$.

Consider a block kept on an inclined plane (inclined at $45°$) as shown in the figure. If the force required to just push it up the incline is $2$ times the force required to just prevent it from sliding down, the coefficient of friction between the block and inclined plane $(\mu )$ is equal to :

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