Question

If a is the acceleration of mass M then find the magnitude of 2$\times$a. Given as M=5 kg, m=3 kg and g=10 m/s${}^2$(downward)

• A. 5
• B. 10
• C. 15
• D. 20

Answer 1

The correct option is A 5

Because the acceleration of the rope is of the same magnitude at every point in the rope, the acceleration of the two masses will also be of equal magnitude. If we label the acceleration of mass m as $a$ , then the acceleration of mass M is $a$. Using Newtons Second Law we find:
For mass M : $Mg-T=ma$
for mass m : $T-mg=ma$
By subtracting the first equation from the second, we find $(M-m)g=(M+m)a$

$⟹a=\frac{M-m}{M+m}g$

Because $M-m>0$ , a is positive and mass m accelerates upward as anticipated. This result gives us a general formula for the acceleration of any pulley system with unequal masses, M and m . Remember, the acceleration is positive for m and negative for M , since m is moving up and M is going down.