A sphere of mass 25 gram is placed on a vertical spring. It is compressed by $$0.2 \mathrm{~m}$$ using a force $$5 \mathrm{~N}$$. When the spring is released, the sphere will reach a height of $$\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right)$$ $$2 \mathrm{~m}$$

A vehicle of mass $$m$$ is moving with momentum $$p$$ on a rough horizontal road. The coefficient of friction between the tyres and the horizontal road is $$\mu$$. The stopping distance is ($$g=$$ acceleration due to gravity)

If the radius of the circular path and frequency of revolution of a particle of mass $m$ are doubled, then the change in its kinetic energy will be $\left(E_i\right.$ and $E_1$ are the initial and final kinetic energies of the particle respectively,)

A force $(F)=-5 \hat{\mathbf{i}}-7 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ acting on a particle causes a displacement $(s)=3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+a \hat{\mathbf{k}}$ in its own direction. If the work done is 14 J , then the value of ' $a$ ' is