A needle is $$7 \mathrm{~cm}$$ long. Assuming that the needle is not wetted by water, what is the weight of the needle, so that it floats on water?

$$\left[\mathrm{T}=\right.$$ surface tension of water $$\left.=70 \frac{\mathrm{dyne}}{\mathrm{cm}}\right]$$

[acceleration due to gravity $$=980 \mathrm{~cm} \mathrm{~s}^{-2}$$]

A driver applies the brakes on seeing the red traffic signal $$400 \mathrm{~m}$$ ahead. At the time of applying the brakes, the vehicle was moving with $$15 \mathrm{~m} / \mathrm{s}$$ and retarding at $$0.3 \mathrm{~m} / \mathrm{s}^2$$. The distance covered by the vehicle from the traffic light 1 minute after the application of brakes is

An ideal gas having molar mass '$$\mathrm{M}_0$$', has r.m.s. velocity 'V' at temperature 'T'. Then

A step down transformer is used to reduce the main supply from '$$V_1$$' volt to '$$V_2$$' volt. The primary coil draws a current '$$\mathrm{I}_1$$' $$\mathrm{A}$$ and the secondary coil draws '$$\mathrm{I}_2$$' A. $$(\mathrm{I}_1<\mathrm{I}_2)$$. The ratio of input power to output power is