A particle experiences a variable force $\overrightarrow{F}=\left(4x\hat{\mathrm{i}}+3y^2\hat{\mathrm{j}}\right)$ in a horizontal $x-y$ plane. Assume distance in meters and force is newton. If the particle moves from point $\left(1, 2\right)$ to point $\left(2, 3\right)$ in the $x-y$ plane, then Kinetic Energy changes by :

A ball of mass $100 \mathrm{g}$ is dropped from a height $h=10 \mathrm{cm}$ on a platform fixed at the top of a vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance $\frac{h}{2}$. The spring constant is _____ $\mathrm{N} {\mathrm{m}}^{-1}$
(Use $g=10{ \mathrm{m} \mathrm{s}}^{-2}$)

Arrange the four graphs in descending order of total work done; where $W_1,W_2,W_3$ and $W_4$ are the work done corresponding to figure $a,b,c$ and $d$ respectively.

A ball is released from rest from point $P$ of a smooth semi-spherical vessel as shown in figure. The ratio of the centripetal force and normal reaction on the ball at point $Q$ is $A$ while angular position of point $Q$ is $\alpha$ with respect to point $P$. Which of the following graphs represent the correct relation between $A$ and $\alpha$ when ball goes from $Q$ to $R$?

A pendulum of length $2 \mathrm{m}$ consists of a wooden bob of mass $50 \mathrm{g}$. A bullet of mass $75 \mathrm{g}$ is fired towards the stationary bob with a speed $v$. The bullet emerges out of the bob with a speed $\frac{v}{3}$ and the bob just completes the vertical circle. The value of $v$ is _____  $\mathrm{m} {\mathrm{s}}^{-1}$

(Take, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$).