Question

Three masses of 2 kg, 4 kg and 3 kg are attached
with light strings over massless pulley as shown in
figure. The pulley itself is attached to a light spring balance. When masses start moving

the reading of the spring balance will be
(2) Less than 9 kg
(4) Zero
(1) Equal to 9 kg
(3) More than 9 kg
​

Answer 1

Answer:

Less than 9 kg.

Explanation:

Given:

Masses, M

M1 = 2 kg

M2 = 4 kg

M3 = 3 kg

From the diagram,

As the string is light and pulley is massless, the tension T is same in whole string. Acceleration due to gravity, g = 10 m/s²

Let the acceleration be 'a'.

For the mass M1, as the mass will move upward,

T - M1g = M1a

T - (2 × 10) = 2a

T - 20 = 2a (Equation 1)

For the mass M2 and M3, as the masses will go downward,

(M2 + M3)g - T = (M2 + M3)a

(4 + 3)10 - T = (4 + 3)a

70 - T = 7a (Equation 2)

Adding equation 1 and 2

70 - T + T - 20 = 7a + 2a

50 = 9a

a = 50/9 m/s²

Putting this value in Equation 1

T - 20 = 2a

T = 2a + 20

T = 2 (50/9) + 20

T = 100/9 + 20

T = (100 + 180)/9

T = 280/9 N

Now we know, the spring is attached to the pulley which is bearing the tension of the string from both the side, so the spring will show a reading of 2Tg i.e.

= 2 × (280/9)

So the reading in the spring is 560/9g = 560/90 = 56/9 = 6.22 kg

So the correct option is 'less than 9 kg'.