A gas balloon is going up with a constant velocity of $10 \mathrm{~m} / \mathrm{s}$. When this balloon reached a height of 75 m , a stone is dropped from it and balloon keeps moving up with the same velocity. The height of the balloon when the stone hits the ground is $\_\_\_\_$ m. (Take $g=10 \mathrm{~m} / \mathrm{s}^2$ )

A thin biconvex lens is prepared from the glass $(\mu=1.5)$ both curved surfaces of which have equal radii of 20 cm each. Left side surface of the lens is silvered from outside to make it reflecting. To have the position of image and object at the same place, the object should be placed, from the lens at a distance of $\_\_\_\_$ cm.

Two identical bodies, projected with the same speed at two different angles cover the same horizontal range $R$. If the time of flight of these bodies are 5 s and 10 s , respectively, then the value of $R$ is

$\_\_\_\_$ m.  (Take $g=10 \mathrm{~m} / \mathrm{s}^2$ )

A solid cylinder having radius $R$ and length $L$ is slipping on a rough horizontal plane. At time $t=0$ the cylinder has a translational velocity $v_{\mathrm{o}}=49 \mathrm{~m} / \mathrm{s}$, perpendicular to its axis and a rotational velocity $v_{\mathrm{o}} / 4 R$ about the centre. The time taken by the cylinder to start rolling is $\_\_\_\_$ seconds. (coefficient of kinetic friction $\mu_K=0.25$ and $g=9.8 \mathrm{~m} / \mathrm{s}^2$ )