An object of mass $$1 \mathrm{~kg}$$ is allowed to hang tangentially from the rim of the wheel of radius R. When released from the rest, the block falls vertically through $$4 \mathrm{~m}$$ height in 2 seconds. The moment of inertia is $$1 \mathrm{~kg} \mathrm{~m}^2$$. The radius of the wheel $$\mathrm{R}$$ is

A planet has double the mass of the earth and double the radius. The gravitational potential at the surface of the Earth is $$\mathrm{V}$$ and the magnitude of the gravitational field strength is $$\mathrm{g}$$. The gravitational potential and gravitational field strength on the surface of the planet are
| Potential | Field | |
|---|---|---|
| A | V | $$\frac{g}{4}$$ |
| B | 2V | $$\frac{g}{2}$$ |
| C | V | $$\frac{g}{2}$$ |
| D | 2V | $$\frac{g}{4}$$ |
A tuning fork of unknown frequency produces 4 beats with tuning fork of frequency $$310 \mathrm{~Hz}$$. It gives the same number of beats on filing. The initial frequency of a tuning fork is
A wire ' 1 ' $$\mathrm{cm}$$ long bent into a circular loop is placed perpendicular to the magnetic field of flux density '$$B^{\prime} W b \mathrm{~m}^{-2}$$. Within $$0.1 \mathrm{sec}$$, the loop is changed into a square of side '$$a$$' $$\mathrm{cm}$$ and flux density is doubled. The value of e.m.f. induced is
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