Question

what is it's answer​

Answer 1

Solution :

➡ Given:

✏ A pulley system of mass m and 2m.

➡ To Find:

✏ Acceleration of mass m.

➡ Force equations:

• For block of mass 2m:

$\implies \rm \: 2mg - T = 2m \times 2a = 4ma \\ \\ \implies \rm \: T = 2mg - 4ma \\ \\ \implies \rm \red{T = 2m(g - 2a)}.....(1)$

• For block of mass m:

$\implies \rm \: 2T - mgsin30 \degree = ma \\ \\ \implies \rm \: 2T = ma + \frac{mg}{2} \\ \\ \implies \rm \: \blue{T = \frac{m}{2} (a + \frac{g}{2} )}.....(2)$

➡ Calculation:

✏ Comparing both equations...

$\mapsto \rm \: 2 \cancel{m}(g - 2a) = \frac{ \cancel{m}}{2} (a + \frac{g}{2} ) \\ \\ \mapsto \rm \: 4g - 8a = a + \frac{g}{2} \\ \\ \mapsto \rm \: 4g - \frac{g}{2} = 9a \\ \\ \mapsto \rm \frac{7g}{2} = 9a \\ \\ \mapsto \rm \: 7g = 18a \\ \\ \mapsto \: \underline{ \boxed{ \bold{ \rm{ \orange{a = \frac{7g}{18} \: \frac{m}{ {s}^{2} } }}}}} \: \star$

Answer 2

$\large \underline{ \red{ \boxed{ \bf \orange{Required \: Answer}}}}$