A block rests on a rough inclined plane making an angle of $30 ^ { \circ }$ with the horizontal. The coefficient of static friction between the block and the plane is 0.8 . If the frictional force on the block is 10 N , the mass of the block (in kg ) is (take $\mathrm { g } = 10 \mathrm {~m} / \mathrm { s } ^ { 2 }$ )
(1) 2.0
(2) 4.0
(3) 1.6
(4) 2.5

A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?
(1) 3.0 cm
(2) 2.0 cm
(3) 1.5 cm
(4) 1.0 cm

A small ball of mass $m$ starts at a point $A$ with speed $v_o$ and moves along a frictionless track $AB$ as shown. The track BC has coefficient of friction $\mu$. The ball comes to stop at C after travelling a distance $L$ which is:
(1) $\frac{2\mathrm{~h}}{\mu} + \frac{\mathrm{v}_\mathrm{o}^2}{2\mu\mathrm{~g}}$
(2) $\frac{\mathrm{h}}{\mu} + \frac{\mathrm{v}_0^2}{2\mu\mathrm{~g}}$
(3) $\frac{\mathrm{h}}{2\mu} + \frac{\mathrm{v}_\mathrm{o}^2}{\mu\mathrm{g}}$
(4) $\frac{\mathrm{h}}{2\mu} + \frac{\mathrm{v}_\mathrm{o}^2}{2\mu\mathrm{g}}$

A body of mass $m$ dropped from a height $h$ reaches the ground with a speed of $0.8 \sqrt { g h }$. The value of work done by the air-friction is:
(1) $- 0.68 m g h$
(2) $m g h$
(3) 0.64 mgh
(4) 1.64 mgh

The bob of a pendulum was released from a horizontal position. The length of the pendulum is 10 m. If it dissipates $10 \%$ of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is: [Use, $g = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }$]
(1) $6 \sqrt { 5 } \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(2) $5 \sqrt { 6 } \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(3) $5 \sqrt { 5 } \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(4) $2 \sqrt { 5 } \mathrm {~m} \mathrm {~s} ^ { - 1 }$

If a rubber ball falls from a height $h$ and rebounds upto the height of $h / 2$. The percentage loss of total energy of the initial system as well as velocity of ball before it strikes the ground, respectively, are :
(1) $50 \% , \sqrt { 2 \mathrm { gh } }$
(2) $50 \% , \sqrt { \mathrm { gh } }$
(3) $40 \% , \sqrt { 2 \mathrm { gh } }$
(4) $50 \% , \sqrt { \frac { \mathrm { gh } } { 2 } }$