A boy stands on a weighing machine inside a lift. When the lift is going down with acceleration $g / 4$, the machine shows a reading 30 kgf. When the lift goes upwards with acceleration $g / 4$, the reading would be

• A

  $18 \mathrm{kgf}$
• B

  $37.5 \mathrm{kgf}$
• Correct answer
  C

  $50 \mathrm{kgf}$
• D

  $67.5 \mathrm{kgf}$

Solution

While going down, machine reading is $30 \mathrm{kgf}$. $\begin{aligned} & \Rightarrow m g-N=m\left(\frac{g}{4}\right) \\ & m g-30 g=\frac{m g}{4} ; 3 \frac{m g}{4}=30 g \\ & m=\frac{30 \times 4}{3}=40 \mathrm{~kg}\end{aligned}$
While going up, the reaction would be $\begin{aligned} & N^{\prime}-m g=m \frac{g}{4} \\ & N^{\prime}=5 \frac{m g}{4}=\frac{5}{4}(40 \mathrm{~kg}) g \\ \Rightarrow \quad N^{\prime} & =50 \mathrm{kgf} .\end{aligned}$

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