A particle is moved from $(0, 0)$ to $(a, a)$ under a force $\vec F = (3\hat i + 4\hat j)$ from two paths. Path $1$ is $OP$ and path $2$ is $OQP$. Let $W_1$ and $W_2$ be the work done by this force in these two paths respectively. Then

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

A block of mass $1\,kg$ is pushed up a surface inclined to horizontal at an angle of $30^o$ by a force of $10\,N$ parallel to the inclined surface (figure). The coefficient of friction between block and the incline is $0.1$. If the block is pushed up by $10\,m$  along the inclined calculate 

$(a)$ work done against gravity

$(b)$ work done against force of friction

$(c)$ increases in potential energy

$(d)$ increases in kinetic energy

$(e)$ work done by applied force

A bomb of mass $9\, kg$ explodes into two pieces of masses $3\, kg$ and $6\, kg$. The velocity of mass $3\, kg$ is $16\, m/s$. The $KE$ of mass $6\, kg$ (in joule) is

If the momentum of a body increases by $0.01\%$, its kinetic energy will increase by ……….. $\%$