A block of mass $m(=0.1 \mathrm{kg})$ is hanging over a frictionless light fixed pulley by an inextensible string of negligible mass. The other end of the string is pulled by a constant force $F$ in the vertically downward direction. The linear momentum of the block increases by $2 \mathrm{kgms}^{-1}$ in $1 \mathrm{s}$ after the block starts from rest. Then, (given $g=10 \mathrm{ms}^{-2}$ )

• Correct answer
  A

  The tension in the string is $F$
• Correct answer
  B

  The tension in the string is $3 \mathrm{N}$
• C

  The work done by the tension on the block is $20 \mathrm{J}$ during this 1 s
• Correct answer
  D

  The work done against the force of gravity is $10 \mathrm{J}$

Solution

The free body diagram $\Rightarrow \quad F=2+m g=3 N$ also, $a=\frac{\text { unbalanced force }}{\text { mass }}=\frac{2}{0.1}=20 \mathrm{m} / \mathrm{s}^{2}$ $S=\frac{1}{2} a t^{2}=\frac{1}{2} \times 20 \times 1=10 \mathrm{m}$ Honce, work done by tension $$ =F \times 10=3 \times 10=30 \mathrm{J} $$ So, the work done against gravity $$ =m g \times S=1 \times 10=10 \mathrm{J} $$

Hence, the correct answer is options: 'A', 'B', 'D'.