The bob of simple pendulum of length '$$L$$' is released from a position of small angular displacement $$\theta$$. Its linear displacement at time '$$\mathrm{t}$$' is ( $$\mathrm{g}=$$ acceleration due to gravity)

The value of acceleration due to gravity at a depth '$$d$$' from the surface of earth and at an altitude '$$h$$' from the surface of earth are in the ratio

A magnetic field of $$2 \times 10^{-2} \mathrm{~T}$$ acts at right angles to a coil of area $$100 \mathrm{~cm}^2$$ with 50 turns. The average e.m.f. induced in the coil is $$0.1 \mathrm{~V}$$, when it is removed from the field in time '$$t$$'. The value of '$$t$$' is

In Young's double slit experiment, $$8^{\text {th }}$$ maximum with wavelength '$$\lambda_1$$' is at a distance '$$d_1$$' from the central maximum and $$6^{\text {th }}$$ maximum with wavelength '$$\lambda_2$$' is at a distance '$$\mathrm{d}_2$$'. Then $$\frac{\mathrm{d}_2}{\mathrm{~d}_1}$$ is