The work done in pulling up a block of wood weighing 2 kN for a length of 10 m on a smooth plane inclined at an angle of $15^{\circ}$ with the horizontal is

• A

  9.82 kJ
• B

  89 kJ
• C

  4.35 kJ
• Correct answer
  D

  5.17 kJ

Solution

Here : Weight of block $w=2 \mathrm{kN}$, Distance $d=10 \mathrm{~m}$ Angle of inclination on the plane $\alpha=15^{\circ}$ The block will be pulled up on a smooth plane Hence, force of resistance due to inclination $\begin{aligned} F & =w \sin \alpha=2 \times 10^3 \sin 15^{\circ} \\ & =2 \times 10^3 \times 0.2588 \\ & =0.5176 \mathrm{kN}\end{aligned}$ Now work done, $\begin{aligned}W=F d & =0.5176 \times 10^3 \times 10 \\& =5.17 \mathrm{kJ}\end{aligned}$

Hence, the correct answer is option: 'D'.