Two masses M1 and M2 are attached to the ends of string which passes over the pulley attached to the top of a double inclined plane. The angles of inclination of the inclined planes are α and β. If M1 = M2 and α = β, the acceleration of the system is

Question

Two masses M1 and M2 are attached to the ends of string which passes over the pulley attached to the top of a double inclined plane. The angles of inclination of the inclined planes are α and β. If M1 = M2 and α = β, the acceleration of the system is (A) zero (B) 2.5 ms-1 (C) 5 ms-2 (D) 10 ms-1

Tardigrade Admin · Accepted Answer

Figure shows a smooth double inclined plane. Two masses

M_{1}

and

M_{2}

are connected with a massless string passing over the pulley as shown in the figure. Let the mass

M_{1}

be accelerating downwards at the rate

a

. Then the mass

M_{2}

will accelerate at the same rate upwards. The equation of motion of

M_{1}

will be

M_{1}

g sin

α

- T =

M_{1}

a ...(1)
And that of mass

M_{2}

will be
T -

M_{2} g

sin

β

=

M_{2}

a .....(2)
To find a , we add equations (1) and (2) . That is :

M_{1} g

sin

α - M_{2} g

sin

β

=

(M_{1} + M_{2}) a

This gives ;

a = \frac{M _{1} s in α - M _{2} s in β}{M _{1} + M _{2}} g

To find tension T, we substitute the value of a in equation (1) and find :

T = \frac{M _{1} M _{2}}{M _{1} + M _{2}} (s in α + s in β) g

If the double inclined plane itself is placed in a compartment accelerating at the rate f , then

a = \frac{M _{1} s in α - M _{2} s in β}{M _{1} + M _{2}} (g - f)

and

T = \frac{M _{1} M _{2}}{M _{1} + M _{2}} (s in α + s in β) (g - f)

Q. Two masses $M_{1}$ and $M_{2}$ are attached to the ends of string which passes over the pulley attached to the top of a double inclined plane. The angles of inclination of the inclined planes are $α$ and $β$ . If $M_{1}$ = $M_{2}$ and $α$ = $β$ , the acceleration of the system is

zero

$2.5 m s^{- 1}$

$5 m s^{- 2}$

$10 m s^{- 1}$

Q. Two masses M1​ and M2​ are attached to the ends of string which passes over the pulley attached to the top of a double inclined plane. The angles of inclination of the inclined planes are α and β. If M1​ = M2​ and α = β, the acceleration of the system is

zero

2.5ms−1

5ms−2

10ms−1

Q. Two masses $M_{1}$ and $M_{2}$ are attached to the ends of string which passes over the pulley attached to the top of a double inclined plane. The angles of inclination of the inclined planes are $α$ and $β$ . If $M_{1}$ = $M_{2}$ and $α$ = $β$ , the acceleration of the system is

$2.5 m s^{- 1}$

$5 m s^{- 2}$

$10 m s^{- 1}$