# Two blocks of masses m1 and m2 connected by a string and placed on an rough inclined plane having coefficient of friction…

Q: Two blocks of masses m1 and m2 connected by a string and placed on an rough inclined plane having coefficient of friction μ as shown in figure. The ratio of masses m1/m2 so that the block m1 starts moving downward.

(a) $\displaystyle \frac{m_1}{m_2} > (\mu cos\theta – sin\theta )$

(b) $\displaystyle \frac{m_1}{m_2} > ( sin\theta +\mu cos\theta )$

(c) $\displaystyle \frac{m_1}{m_2} > ( cos\theta – \mu sin\theta )$

(b) $\displaystyle \frac{m_1}{m_2} > ( sin\theta -\mu cos\theta )$

Ans: (a)

Sol: As block m1 starts moving downwards , so

$\displaystyle m_2 g sin\theta > \mu N + m_1 g$

$\displaystyle m_2 g sin\theta > \mu m_2 g cos\theta + m_1 g$

$\displaystyle m_2 g (sin\theta – \mu cos\theta ) > m_1 g$

$\displaystyle m_2 (sin\theta – \mu cos\theta ) > m_1$

$\displaystyle (sin\theta – \mu cos\theta ) > \frac{m_1}{m_2}$

$\displaystyle – ( \mu cos\theta – sin\theta ) > \frac{m_1}{m_2}$

$\displaystyle ( \mu cos\theta – sin\theta ) < \frac{m_1}{m_2}$