Question

Two masses M 1 ​ and M 2 ​ are attached to the end of a light string which passes over a massless pulley attached to the top of a double inclined smooth plane of angles of inclination α and β. If M 2 ​ >M 1 ​ and β>α then the acceleration of block M 2 ​ down the inclined will be: question

Answer 1

QUESTIONS

Two masses M 1 and M 2 are attached to the end of a light string which passes over a massless pulley attached to the top of a double inclined smooth plane of angles of inclination α and β. If M 2 >M 1 and β>α then the acceleration of block M 2 down the inclined will be: question

ANSWER

First draw the free body diagram of the given figure

note the following—

1)Mass $M_{1}$ has its acceleration in upward direction.

2)Mass $M_{2}$ has its acceleration in downward direction.

3)Tension will remain same in both the string

now resolving the forces for both the block we find

T- $M_{1}$ g sin α = $M_{1}$a

T- $M_{1}$ g sin β = $M_{2}$a

Hence we substitute the value of T in any of the following we get...

T- $M_{1}$α + $M_{1}$ g sin α

$M_{1}$α + $M_{1}$ g sin α - $M_{2}$ g sin β = $-M_{2}$a

$M_{1}$ g sin α - $M_{2}$ g sin β = -a ($M_{2}$+ $M_{1}$)

$a = \frac{ m_2 \: gsin \alpha - m_{1}gsin \alpha }{ m_{2} + m_{1} }$