Question

I. Acceleration of A with respect to lift is

• A. $\frac{26}{7}$ m/s²
• B. $\frac{20}{7}$ m/s²
• C. $\frac{40}{13}$ m/s²
• D. None

Answer 1

Answer: (A)

$\frac{26}{7}$ m/s²

Answer 2

In the non-inertial frame of the lift, the effective acceleration due to gravity is $g_{eff} = g + a_{lift}$ downwards.

Let $a_{rel}$ be the acceleration of A relative to the lift. Since $m_A > m_B$, A moves downwards relative to the lift and B moves upwards relative to the lift.

Using Newton's second law in the lift frame:

For mass A: $m_A g_{eff} - T = m_A a_{rel}$

For mass B: $T - m_B g_{eff} = m_B a_{rel}$

Adding the two equations: $(m_A - m_B) g_{eff} = (m_A + m_B) a_{rel}$

$a_{rel} = \frac{m_A - m_B}{m_A + m_B} g_{eff} = \frac{10 - 4}{10 + 4} g_{eff} = \frac{6}{14} g_{eff} = \frac{3}{7} g_{eff}$.

Given options for $a_{rel}$, assuming option (A) is correct, so $a_{rel} = \frac{26}{7} \, m/s^2$.

Then $\frac{26}{7} = \frac{3}{7} g_{eff}$, which gives $g_{eff} = \frac{26}{3} \, m/s^2$.

Since $g_{eff} = g + a_{lift}$, we have $\frac{26}{3} = g + 3$.

$g = \frac{26}{3} - 3 = \frac{26 - 9}{3} = \frac{17}{3} \, m/s^2$.