$A$ force $\vec{F} = -5 \hat{i} - 7 \hat{j} + 3 \hat{k}$ acting on a particle causes a displacement $\vec{s} = 3 \hat{i} - 2 \hat{j} + a \hat{k}$. If the work done is $14 \ J$,then the value of '$a$' is:

The figure shows three forces applied to a trunk that moves leftward by $3\, m$ over a smooth floor. The force magnitudes are $F_1 = 5\, N$,$F_2 = 9\, N$,and $F_3 = 3\, N$. The net work done on the trunk by the three forces is ............... $J$.

$A$ particle of mass $100 \ g$ is projected vertically upwards with a speed of $5 \ m/s$. What is the work done by the force of gravity during the time the particle returns to the starting point? (in $J$)

$A$ particle is displaced from point $P(3 \ m, 4 \ m, 5 \ m)$ to a point $Q(2 \ m, 3 \ m, 4 \ m)$ under a constant force $\vec{F}=(3 \hat{i}+4 \hat{j}+5 \hat{k}) \ N$. The work done by the force in this process is

When a body moves in a circular path,no work is done by the centripetal force since

$A$ ball of mass $m$ is attached to a string whose other end is fixed. The system is free to rotate in a vertical plane. When the ball swings,no work is done on the ball by the tension in the string. Which of the following statements is the correct explanation?