The depth from the surface of the earth of radius $$\mathrm{R}$$, at which acceleration due to gravity will be $$60 \%$$ of the value on the earth surface is

A body of mass 'm' is moving with speed 'V' along a circular path of radius 'r'. Now the speed is reduced to $$\frac{V}{2}$$ and radius is increased to '3r'. For this change, initial centripetal force needs to be

The path difference between two interfering light waves meeting at a point on the screen is $$\left(\frac{57}{2}\right) \lambda$$. The bond obtained at that point is

Pressure inside two soap bubbles are 1.01 atm and 1.03 atm. The ratio between their volumes is (Pressure outside the soap bubble is 1 atmosphere)