$A$ block moving horizontally on a smooth surface with a speed of $40 \, m/s$ splits into two equal parts. If one of the parts moves at $60 \, m/s$ in the same direction,then the fractional change in the kinetic energy will be $x: 4$ where $x = ..... .$

$A$ bob of mass $m$,suspended by a string of length $l_1$,is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point,it collides elastically with another bob of mass $m$ suspended by a string of length $l_2$,which is initially at rest. Both the strings are massless and inextensible. If the second bob,after collision,acquires the minimum speed required to complete a full circle in the vertical plane,the ratio $\frac{l_1}{l_2}$ is

Which of the following statements is true for a collision?

Two identical particles are moving with same velocity $v$ as shown in the figure. If the collision is completely inelastic,then:

Two rectangular blocks $A$ and $B$ of masses $2 \,kg$ and $3 \,kg$ respectively are connected by a spring of spring constant $10.8 \,Nm^{-1}$ and are placed on a frictionless horizontal surface. The block $A$ is given an initial velocity of $0.15 \,ms^{-1}$ in the direction shown in the figure. The maximum compression of the spring during the motion is (in $\,m$)

$A$ baseball having mass of $0.4 \ kg$ is thrown such that one of the forces acting on it varies with time as shown in the first graph. Also,the velocity of the ball is in the same direction as the force. The velocity varies with time as shown in the second graph. Choose the incorrect option (up to $0.3 \ s$).