Question

Two masses 8 kg and 12 KG are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses and the tension in the string when the masses are released.

Answer 1

Hii dear,

# Answer-
a = 2 m/s^2
T = 96 N.

## Explaination-
# Given-
m1 = 8 kg
m2 = 12 kg
g = 10 m/s^2

# Solution-
Suppose, two masses be m1 and m2 such that m2>m1.
Also T = tension in string
a = acceleration of m1 (upwards) & m2 (downwards).

Let's get some equations,
T - m1g = m1a ...(1)
m2g - T = m2a ...(2)

Adding eqns & solving them
a = (m2-m1)g/(m1+m2)
a = (12-8)×10/(12+8)
a = 2 m/s^2

Now, solving for T,
T - m1g = m1a
T = m1(a+g)
T = 8(2+10)
T = 96 N.

When realesed, acceleration in the string will be 2 m/s^2 and tension will be 96 N.