Mumbai needs $1.4 \times 10^{12} \, L$ of water annually. Its effective surface area is $600 \, km^2$ and it receives an average rainfall of $2.4 \, m$ annually. If $10 \%$ of this rainwater is conserved,it will meet approximately:

The ratio of the dimension of Planck's constant and that of moment of inertia is the dimension of

The length of a cylinder is measured with a meter rod having a least count of $0.1 \, cm$. Its diameter is measured with vernier calipers having a least count of $0.01 \, cm$. Given that the length is $5.0 \, cm$ and the radius is $2.0 \, cm$,the percentage error in the calculated value of the volume will be ......... $\%$

The diameter of a wire measured by a screw gauge of least count $0.001 \text{ cm}$ is $0.08 \text{ cm}$. The length measured by a scale of least count $0.1 \text{ cm}$ is $150 \text{ cm}$. When a weight of $100 \text{ N}$ is applied to the wire, the extension in length is $0.5 \text{ cm}$, measured by a micrometer of least count $0.001 \text{ cm}$. The error in the measured Young's modulus is $\alpha \times 10^9 \text{ N/m}^2$. The value of $\alpha$ is . . . . . . . (Ignore the contribution of the load to Young's modulus error calculation)

Mention the $MKS$ and $CGS$ units of work,define them,and write the dimensional formula of work.

If the unit of length and force be increased four times,then the unit of energy is