In the figure, the acceleration of m1….

Q: In the figure, the acceleration of m1 (here , mass of block on the table = m1)

 Q & A

(a) $\displaystyle \frac{2m_2 g}{m_1 + m_2} $

(b) $ \displaystyle \frac{2m_2 g}{4m_1 + m_2} $

(c) $ \displaystyle \frac{2m_2 g}{4m_1 – m_2} $

(d) $ \displaystyle \frac{m_2 g}{4m_1 + m_2} $

Ans: (b)
Sol: Let acceleration of m2 = a

Then , Acceleration of m1 = 2 a

For m2 ,

m2 g – 2 T = m2 a …(i)

For m1 ,

T = m1 (2a) …(ii)

From (i)

m2 g – 2 (2 m1 a ) = m2 a

m2 g = (4 m1 + m2)a

$\displaystyle a = \frac{m_2 g}{4 m_1 + m_2} $

Acceleration of m1 = 2 a

$\displaystyle = \frac{ 2 m_2 g}{4 m_1 + m_2} $