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In the system as shown in figure. All surfaces are smooth, strings are light and inextensible. Given $m_{A} = 1 k g : m_{B} = 2 k g : m_{C} = 3 k g, g = 10 m s^{- 2} : K = 50 N m^{- 1},$ The system is released from rest. (Assume that the spring will reach a maximum elongation and remain constant)

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The tension in the string is $\frac{50}{6} N$

Only A and B are correct

Extension in the string is 10cm

The acceleration of the system is $\frac{50}{6} m s^{- 2}$

answer is A, B, C.

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Detailed Solution

(i) Acceleration (a) $= \frac{n e t f o r c e}{n e t m a s s}$

$= \frac{5 g}{6} = \frac{5 \times 10}{6} = \frac{50}{6} m / \sec^{2}$

For 1kg mass T $= m a = 1 (\frac{50}{6}) = \frac{50}{6} N$

For 3kg mass $3 g - T = 3 a \Rightarrow T = 3 (g - a)$

$= 3 (10 - \frac{50}{6})$

=5N

$k x = 5 \Rightarrow x = \frac{5}{k} = \frac{5}{50} = \frac{1}{10} m = 10 c m$

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