A 1 kg block subjected to two simultaneous forces $(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}) \mathrm{N}$ and $(3 \hat{\mathrm{i}}-\hat{\mathrm{j}}-2 \hat{\mathrm{k}}) \mathrm{N}$ is moved a distance of 25 m along $(3 \hat{\mathrm{i}}-4 \hat{\mathrm{j}})$ direction. The work done in this process is $\_\_\_\_$ J.

The surface tension of a soap solution is $3.5 \times 10^{-2} \mathrm{~N} / \mathrm{m}$. The work required to increase the radius of a soap bubble from 1 cm to 2 cm is $\alpha \times 10^{-6} \mathrm{~J}$. The value of $\alpha$ is $\_\_\_\_$ .

$$ (\pi=22 / 7) $$

The velocity of a particle executing simple harmonic motion along $x$-axis is described as $v^2=50-x^2$, where $x$ represents displacement. If the time period of motion is $\frac{x}{7} \mathrm{~s}$, the value of $x$ is $\_\_\_\_$ .

A body of mass 2 kg begins to move under the influence of time dependent force $\overrightarrow{\mathrm{F}}=\left(2 \mathrm{t} \hat{\mathrm{i}}+6 \mathrm{t}^2 \hat{\mathrm{j}}\right) \mathrm{N}$, where $\hat{\mathrm{i}}$ and $\hat{\mathrm{j}}$ are unit vectors along $x$ and y -axis respectively. The power produced by the force at $t=2 \mathrm{~s}$ is $\_\_\_\_$ W.