First slide

Constraints

Question

Two blocks of masses $m_{1} and m_{2}$ are connected as shown in the figure. The acceleration of the block $m_{2}$ , is:

Moderate

A

$\frac{m_{2} g}{m_{1} + m_{2}}$
B

$\frac{m_{1} g}{m_{1} + m_{2}}$
C

$\frac{4 m_{2} g - m_{1} g}{m_{1} + m_{2}}$
D

$\frac{m_{2} g}{m_{1} + 4 m_{2}}$

Solution

Let a = ${acc}^{n} of m_{1}; {acc}^{n} of pulley = \frac{a + 0}{2} = \frac{a}{2}$
If acceleration of $m_{2}$ = b
Then 0+ $\frac{b}{2} = \frac{a}{2}$
Hence a = b
$T = m_{1} a, m_{2} g - T = m_{2} a$
$∴ a = \frac{m_{2} g}{m_{1} + m_{2}}$

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