A block 'A' takes 2 s to slide down a frictionless incline of 30$$^\circ$$ and length 'l', kept inside a lift going up with uniform velocity 'v'. If the incline is changed to 45$$^\circ$$, the time taken by the block, to slide down the incline, will be approximately :

The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at (4 + x) cm inside the block. The value of x is :

A body of mass $$\mathrm{m}$$ is projected with velocity $$\lambda \,v_{\mathrm{e}}$$ in vertically upward direction from the surface of the earth into space. It is given that $$v_{\mathrm{e}}$$ is escape velocity and $$\lambda<1$$. If air resistance is considered to be negligible, then the maximum height from the centre of earth, to which the body can go, will be :

(R : radius of earth)

A steel wire of length $$3.2 \mathrm{~m}\left(\mathrm{Y}_{\mathrm{s}}=2.0 \times 10^{11} \,\mathrm{Nm}^{-2}\right)$$ and a copper wire of length $$4.4 \mathrm{~m}\left(\mathrm{Y}_{\mathrm{c}}=1.1 \times 10^{11} \,\mathrm{Nm}^{-2}\right)$$, both of radius $$1.4 \mathrm{~mm}$$ are connected end to end. When stretched by a load, the net elongation is found to be $$1.4 \mathrm{~mm}$$. The load applied, in Newton, will be: $$\quad\left(\right.$$ Given $$\pi=\frac{22}{7}$$)