Question

two masses 8 kg and 12 kg are
attached to an ideal string passed over
a fixled smooth pulley. When it is
released from rest, what will be the
distance travelled by each mass in
2 second?​

Answer 1

The given system of two masses and a pulley can be represented as shown in the following figure:

Smaller mass, m

1

=8 kg

Larger mass,m

2

=12kg

Tension in the string=T

Mass m

2

, owing to its weight, moves downward with acceleration, and mass m

1

moves upward.

Applying Newton’s second law of motion to the system of each mass:

For mass m 1 :

The equation of motion can be written as:

T–m 1

g=ma… (i)

For mass m2:The equation of motion can be written as:m 2

g–T=m2a … (ii)

Adding equations (i) and (ii), we get:

(m2−m1)g=(m1+m2)a

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Answer 2

The given system of two masses and a pulley can be represented as shown in the following figure:

Smaller mass, m

1

=8 kg

Larger mass,m

2

=12kg

Tension in the string=T

Mass m

2

, owing to its weight, moves downward with acceleration, and mass m

1

moves upward.

Applying Newton’s second law of motion to the system of each mass:

For mass m 1 :

The equation of motion can be written as:

T–m 1

g=ma… (i)

For mass m2:The equation of motion can be written as:m 2

g–T=m2a … (ii)

Adding equations (i) and (ii), we get:

(m2−m1)g=(m1+m2)a