A ball projected from ground at an angle of $45^{\circ}$ just clears a wall in front. If point of projection is 4 m from the foot of wall and ball strikes the ground at a distance of 6 m on the other side of the wall, the height of the wall is: (1) 4.4 m (2) 2.4 m (3) 3.6 m (4) 1.6 m
Two blocks of mass $M_1 = 20\mathrm{~kg}$ and $M_2 = 12\mathrm{~kg}$ are connected by a metal rod of mass 8 kg. The system is pulled vertically up by applying a force of 480 N as shown. The tension at the mid-point of the rod is: (1) 144 N (2) 96 N (3) 240 N (4) 192 N
A body starts from rest on a long inclined plane of slope $45^{\circ}$. The coefficient of friction between the body and the plane varies as $\mu = 0.3x$, where $x$ is distance travelled down the plane. The body will have maximum speed (for $g = 10\mathrm{~m/s^2}$) when $x =$ (1) 9.8 m (2) 27 m (3) 12 m (4) 3.33 m
A tennis ball (treated as hollow spherical shell) starting from O rolls down a hill. At point A the ball becomes air borne leaving at an angle of $30^{\circ}$ with the horizontal. The ball strikes the ground at B. What is the value of the distance AB? (Moment of inertia of a spherical shell of mass $m$ and radius $R$ about its diameter $= \frac{2}{3}mR^2$) (1) 1.87 m (2) 2.08 m (3) 1.57 m (4) 1.77 m
A mass $m = 1.0\mathrm{~kg}$ is put on a flat pan attached to a vertical spring fixed on the ground. The mass of the spring and the pan is negligible. When pressed slightly and released, the mass executes simple harmonic motion. The spring constant is $500\mathrm{~N/m}$. What is the amplitude A of the motion, so that the mass $m$ tends to get detached from the pan? (Take $g = 10\mathrm{~m/s^2}$). The spring is stiff enough so that it does not get distorted during the motion. (1) $\mathrm{A} > 2.0\mathrm{~cm}$ (2) $\mathrm{A} = 2.0\mathrm{~cm}$ (3) $\mathrm{A} < 2.0\mathrm{~cm}$ (4) $\mathrm{A} = 1.5\mathrm{~cm}$