A bullet of mass 20 g has an initial speed of $1 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, just before it starts penetrating a mud wall of thickness 20 cm . If the wall offers a mean resistance of $2.5 \times 10 ^ { - 2 } \mathrm {~N}$, the speed of the bullet after emerging from the other side of the wall is close to: (1) $0.7 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ (2) $0.3 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ (3) $0.1 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ (4) $0.4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
A plane is inclined at an angle $\alpha = 30 ^ { \circ }$ with respect to the horizontal. A particle is projected with a speed $\mathrm { u } = 2 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, from the base of the plane, making an angle $\theta = 15 ^ { \circ }$ with respect to the plane as shown in the figure. The distance from the base, at which the particle hits the plane is close to: (Take $\mathrm { g } = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ ) (1) 20 cm (2) 18 cm (3) 14 cm (4) 26 cm
Two blocks $A$ and $B$ of masses $m _ { A } = 1 \mathrm {~kg}$ and $m _ { B } = 3 \mathrm {~kg}$ are kept on the table as shown in figure. The coefficients of friction between $A$ and $B$ is 0.2 and between $B$ and the surface of the table is also 0.2 . The maximum force F that can be applied on B horizontally, so that the block A does not slide over the block B is : [Take $\mathrm { g } = 10 \mathrm {~m} / \mathrm { s } ^ { 2 }$ ] (1) 16 N (2) 12 N (3) 40 N (4) 8 N
The time dependence of the position of a particle of mass $m = 2$ is given by $\vec { r } t = 2 t \hat { i } - 3 t ^ { 2 } \hat { j }$. Its angular momentum, with respect to the origin, at time $\mathrm { t } = 2$ is: (1) 36 k (2) $48 \hat { i } + \hat { j }$ (3) $- 48 \hat{k}$ (4) $- 34 \mathrm { k } - \hat { \mathrm { i } }$
A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that only gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in 24 hours around the planet? [Given: Mass of planet $= 8 \times 10 ^ { 22 } \mathrm {~kg}$, Radius of planet $= 2 \times 10 ^ { 6 } \mathrm {~m}$, Gravitational constant $\mathrm { G } = 6.67 \times 10 ^ { - 11 } \mathrm { Nm } ^ { 2 } / \mathrm { kg } ^ { 2 }$ ] (1) 17 (2) 9 (3) 13 (4) 11