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Mr. X of mass 80kg enters a lift and selects the floor he wants. The lift now accelerates upwards at $2 {ms}^{- 2}$ for 2s and then moves with constant velocity. As the lift approaches his floor, it decelerates at the same rate as it previously accelerates. If the lift cables can safely withstand a tension of $2 \times 10^{4} N$ and the lift itself has a mass of 500kg, how many $Mr$ . $X^{'} s$ could it safely carry at one time?

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answer is B.

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Detailed Solution

$T - (n m + M) g = (n m + M) a$

$∴ n (m g + m a) = T - M g - M a$

$or n = \frac{T - M (g + a)}{m (g + a)} n_{\max} = \frac{T_{m i x} - M (g + a)}{m (g + a)} = \frac{2 \times 10^{4} - 500 (10 + 2)}{80 (10 + 2)} = 14.58$

But answer will be 14 .

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