Two solid rubber balls $A$ and $B$ have masses $200 \ g$ and $400 \ g$ respectively. They are moving towards each other,with ball $A$ having a velocity of $0.3 \ m/s$. After the collision,both balls come to rest. What is the velocity of ball $B$ in $m/s$?

$A$ particle of mass $m$ is moving along the $x$-axis with initial velocity $u \hat{i}$. It collides elastically with a particle of mass $10m$ at rest and then moves with half its initial kinetic energy (see figure). If $\sin \theta_{1} = \sqrt{n} \sin \theta_{2}$,then the value of $n$ is:

$A$ bullet moving with a velocity of $100\, m/s$ can just penetrate two planks of equal thickness. The number of such planks penetrated by the same bullet,when the velocity is doubled,will be

Identify the correct statements from the following:
$(A)$ Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative.
$(B)$ Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative.
$(C)$ Work done by friction on a body sliding down an inclined plane is positive.
$(D)$ Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity is zero.
$(E)$ Work done by the air resistance on an oscillating pendulum is negative.
Choose the correct answer from the options given below:

$A$ bullet of mass $0.01 \, kg$ travelling at a speed of $500 \, m/s$ strikes a block of mass $2 \, kg$ which is suspended by a string of length $5 \, m$. The center of gravity of the block is found to rise a vertical distance of $0.1 \, m$. What is the speed of the bullet after it emerges from the block?

$300\, J$ of work is done in sliding a $2\, kg$ block up an inclined plane of height $10\, m.$ Work done against friction is.....$J$ (Take $g = 10\, m/s^2$)