Question

In a model hydraulic lift, a force of 1 N is exerted on one arm which moves it by 20 cm. By what distance does the other arm move if the force experienced at the other end is 10 N?

• A. 0.2 cm
• B. 2 cm
• C. 20 cm
• D. 200 cm

Answer 1

The correct option is B

2 cm

From the principle of conservation of energy, work done at both ends of the hydraulic lift is the same.

Let $F_1$ and $F_2$ be the forces and $x_1$ and $x_2$ be the displacements at each end of the lift respectively.

Then,
Work done at the first end, $W_1=F_1\times x_1$
Work done at the second end, $W_2=F_2\times x_2$
$W_1=W_2$
$\Rightarrow F_1\times x_1=F_2\times x_2$
Therefore, $1\times 20=10\times x_2$
$\Rightarrow x_2=\frac{1\times 20}{10}=2cm$

Hence, other arm moves by $2cm$