A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity $$4 \mathrm{~m} \mathrm{~s}^{-1}$$. The ball strikes the water surface after $$4 \mathrm{~s}$$. The height of bridge above water surface is (Take $$g=10 \mathrm{~m} \mathrm{~s}^{-2}$$ )
Two thin lenses are of same focal lengths $$(f)$$, but one is convex and the other one is concave. When they are placed in contact with each other, the equivalent focal length of the combination will be :
A wire carrying a current $$I$$ along the positive $$\mathrm{x}$$-axis has length $$L$$. It is kept in a magnetic field $$\overrightarrow{\mathrm{B}}=(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-4 \hat{\mathrm{k}}) \mathrm{T}$$. The magnitude of the magnetic force acting on the wire is :
A bullet from a gun is fired on a rectangular wooden block with velocity $$u$$. When bullet travels $$24 \mathrm{~cm}$$ through the block along its length horizontally, velocity of bullet becomes $$\frac{u}{3}$$. Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is :