Consider a block and trolley system as shown in figure. If the coefficient of kinetic friction between the trolley and the surface is 0.04, the acceleration of the system in $\mathrm { m } \mathrm { s } ^ { - 2 }$ is: (Consider that the string is massless and unstretchable and the pulley is also massless and frictionless): (1) 3 (2) 4 (3) 2 (4) 1.2
A simple pendulum of length 1 m has a wooden bob of mass 1 kg. It is struck by a bullet of mass $10 ^ { - 2 } \mathrm {~kg}$ moving with a speed of $2 \times 10 ^ { 2 } \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The bullet gets embedded into the bob. The height to which the bob rises before swinging back is. (use $g = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }$) (1) 0.30 m (2) 0.20 m (3) 0.35 m (4) 0.40 m
A ball of mass 0.5 kg is attached to a string of length 50 cm. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is 400 N. The maximum possible value of angular velocity of the ball in rad $\mathrm { s } ^ { - 1 }$ is,: (1) 1600 (2) 40 (3) 1000 (4) 20
A particle is moving in one dimension (along $x$ axis) under the action of a variable force. It's initial position was 16 m right of origin. The variation of its position $x$ with time $t$ is given as $x = - 3 t ^ { 3 } + 18 t ^ { 2 } + 16t$, where $x$ is in m and $t$ is in s. The velocity of the particle when its acceleration becomes zero is $\_\_\_\_$ $\mathrm { m } \mathrm { s } ^ { - 1 }$.
The identical spheres each of mass $2M$ are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 4 m each. Taking point of intersection of these two sides as origin, the magnitude of position vector of the centre of mass of the system is $\frac { 4 \sqrt { 2 } } { x }$, where the value of $x$ is $\_\_\_\_$.