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Home » 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.
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.
CBSE | Class 11 | Laws of Motion | NCERT | Physics
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.

According to the question,

m1 = 8 kg

m2 = 12 kg

Tension = T

The heavier mass m2 will move downwards and the smaller mass m1 will move upwards.

On Applying Newton’s second law,

For mass m1:

T – m1g = m1a —– (1)

For mass m2:

m2g – T = m2a ——(2)

Add (1) and (2)

(m2 – m1) g = (m1 + m2) a

a = (m2 – m1) g/ (m1 + m2)

=[ (12 – 8)/(12 + 8)] x 10 = (4 /20) x 10= 2m/s

Therefore, acceleration of the mass is 2 m/s2

m2g – T = m2a

m2g – T = m2 [ (m2 – m1) g/ (m1 + m2) ]

= 2m1m2g/(m1 + m2)

T = 2 x 12 x 8 x 10/ (12 + 8)

T = 96 N

Hence,  the tension on the string is 96 N

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