A body of mass \(2 \mathrm{~kg}\) moving vertical upwards has its velocity increased uniformly from \(10 \mathrm{~ms}^{-1}\) to \(40 \mathrm{~ms}^{-1}\) in 4seC. Neglecting air resistance, calculate the upward vertical force acting on the body. \(\left(g=10 \mathrm{~ms}^{-2}\right)\).
A. \(15 \mathrm{~N}\) B. \(20 \mathrm{~N}\) C. \(35 \mathrm{~N}\) D. \(45 N\)
Correct Answer: D
Explanation
\(\mathrm{a}=\frac{v-u}{\mathrm{t}}=\left(\frac{40-10}{4}\right) \mathrm{m} / \mathrm{s}^2=7.5 \mathrm{~m} / \mathrm{s}^2\) one has to be careful here! \(f eq m a\) you can't get the required upward force by multiplying the mass and the acceleration. This would have been the case if it were translational (horizontal) motion. The force to be applied must be sufficient to give the calculated upward acceleration as well as annihilate the downward gravity drag. Then, We write Fnet=ma i.e \begin{aligned} \mathrm{f}_{\mathrm{u}}-\mathrm{f}_{\mathrm{g}} &=m a \\ \mathrm{f}_{\mathrm{u}} &=m a+\mathrm{f}_{\mathrm{g}} \\ &=m a+\mathrm{m} \\ &=m a+m g \\ &=m(a+g) \\ &=2(7.5+10) \\ &=2(17.5) \\ &=35 \mathrm{~N} \end{aligned}