A pulley system is attached to an elevator as shown in figure- The elevator starts to move up with an acceleration a-Match statements in column I with results in column II- Column I Column II- a Acceleration of m1 in elevator frame p 12 m2-m1g-2m2am1-m2 t2- b Acceleration of m1 in ground frame q 12 - m2 -m1m1-m2g-a -t2- c Distance covered of m1 in elevator frame r m2-m1m1-m2 g- 2m2m1-m2 a- d Distance covered of m1 in ground frame s m2-m1m1-m2g-a- t None of the above- -

Consider an observer in elevator frame, From figure, T m_1 (a+g)=m_1 a_1 nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp;... (1) m_2 (a+g) T=m_2 ...

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Byju's Answer

Standard XIII

Physics

Problems with Pseudo Force

A pulley syst...

Question

A pulley system is attached to an elevator as shown in figure. The elevator starts to move up with an acceleration $a$ .

Match statements in column I with results in column II.
$\begin{matrix} Column I & Column II (a) & Acceleration of m_{1} in elevator frame & (p) & \frac{1}{2} (\frac{(m_{2} - m_{1}) g + 2 m_{2} a}{m_{1} + m_{2}}) t^{2} (b) & Acceleration of m_{1} in ground frame & (q) & \frac{1}{2} [\frac{m_{2} - m_{1}}{(m_{1} + m_{2})} (g + a)] t^{2} (c) & Distance covered of m_{1} in elevator frame & (r) & (\frac{m_{2} - m_{1}}{m_{1} + m_{2}}) g + (\frac{2 m_{2}}{m_{1} + m_{2}}) a (d) & Distance covered of m_{1} in ground frame & (s) & \frac{(m_{2} - m_{1})}{(m_{1} + m_{2})} (g + a) (t) & None of the above \end{matrix}$

a - s; b - r; c - q; d - p

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a - r; b - q; c - p; d - s

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a - s; b - t; c - q; d - t

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a - r; b - q; c - s; d - p

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Solution

The correct option is A a - s; b - r; c - q; d - p

Consider an observer in elevator frame,

From figure,
$T - m_{1} (a + g) = m_{1} a_{1}$ ... (1)
$m_{2} (a + g) - T = m_{2} a_{1}$ ... (2)
From (1) and (2),
$m_{2} (a + g) - m_{1} (a + g) = (m_{1} + m_{2}) a_{1}$
$∴ a_{1} = \frac{(m_{2} - m_{1}) (a + g)}{(m_{1} + m_{2})}$
Distance covered in elevator frame
$= \frac{1}{2} (\frac{(m_{2} - m_{1}) (a + g)}{(m_{1} + m_{2})}) \times t^{2}$

In ground frame,

$a_{1} + a = \frac{m_{2} a - m_{1} a + g m_{2} - g m_{1} + a m_{1} + m_{2} a}{(m_{1} + m_{2})} = (\frac{m_{2} - m_{1}}{m_{1} + m_{2}}) g + (\frac{2 m_{2}}{m_{1} + m_{2}}) a$

Distance covered in ground frame $= \frac{1}{2} (\frac{(m_{2} - m_{1}) g + 2 m_{2} a}{m_{1} + m_{2}}) t^{2}$

(a) → (s); (b) → (r); (c) → (q); (d) → (p)

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