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Standard XII

Physics

Capacitance of a Random Conductor

In a simple w...

Question

In a simple wood machine, two unequal masses $m_{1}$ and $m_{1}$ are connected by a string going over a clamped light smooth pulley. In a typical arrangement (In the figure) $m_{1} = 300 g$ and $m_{2} = 600 g$ . The system is released from rest.

7.8 N

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8.7 N

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5.1 N

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2.1 N

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Solution

The correct option is A 7.8 N
For block 1
$T - (m_{1} g + m_{1} a) = 0 - - - - - - (1)$
$T = m_{1} g + m_{1} a$

For block 2,
$T + m_{2} a - m_{2} g = 0$ ---------- (2)
$T = m_{2} g - m_{2} a$
From en (1) and (2),
$m_{1} g + m_{1} a + m_{2} a - m_{2} g = 0$
From eqn (1) $a (m_{1} + m_{2}) = g (m_{2} - m_{1})$
$a = g (\frac{m_{2} - m_{1}}{m_{1} + m_{2}})$
$a = 9.8 (\frac{0.6 - 0.3}{0.6 + 0.3}) = 3.260 m / s^{2}$

(a) T= 2s, a= 3.260 m/ $s^{2}$ , speed u=0
$s = u t + \frac{1}{2} a t^{2}$
$= 0 + \frac{1}{2} ({3.260)}^{2} \times 2^{2} = 6.5 m$

(b) From (1), $T = m_{1} (g + a) = 0.3 (9.8 + 3.260) = 3.9 N$
(C)F-2T=0
F=2T= $2 \times 3.9 = 7.8 N$

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Figure

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In a simple wood machine, two unequal masses m1 and m1 are connected by a string going over a clamped light smooth pulley. In a typical arrangement (In the figure) m1=300g and m2=600g. The system is released from rest.

In a simple wood machine, two unequal masses $m_{1}$ and $m_{1}$ are connected by a string going over a clamped light smooth pulley. In a typical arrangement (In the figure) $m_{1} = 300 g$ and $m_{2} = 600 g$ . The system is released from rest.