Question

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

Answer 1

The tension in the string is 96 N.

Explanation:

Given data:

• Smaller mass, m1 = 8 kg
• Larger mass, m2 = 12 kg
• Tension in the string = T

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

For mass m1:

The equation of motion can be written as:

T – m1g = ma … (1)

For mass m2:

The equation of motion can be written as:

m2g – T = m2a … (2)

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

(m2 - m1)g = (m1 + m2)a

a = ( (m2 - m1) / (m1 + m2) )g    ....(3)

= (12 - 8) / (12 + 8) × 10  =  4 × 10 / 20  =  2 ms-2

Therefore, the acceleration of the masses is 2 m/s^2.

Substituting the value of a in equation (ii), we get:

m2g - T = m2(m2 - m1)g / (m1 + m2)

T = (m2 - (m2^2 - m1m2) / (m1 + m2) )g

= 2m1m2g / (m1 + m2)

= 2 × 12 × 8 × 10 / (12 + 8)

= 96 N

Therefore, the tension in the string is 96 N.

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Answer 2

Answer:

• Tension (T) in the string is 96 N.

Given:

1. Mass of lighter block (M₁) = 8 Kg
2. Mass of Higher block (M₂) = 12 kg.
3. Let the Tension be " T "
4. Let the Acceleration be " a "

Explanation:

________________________

Since, M₂ is Heavier ( 12 Kg > 8 Kg ) so it will pull the system Downwards.

# Refer the Attachment for Figure.

Now, Applying Law of Equilibrium For 8 Kg Block.

Equation will be,

⟼ T - M₁g = Ma

Substituting the Values,

⟼ T - 8 x 10 = 8 x a

⟼ T - 80 = 8 a

⟼ T = 8 a + 80  ___ [1]

Now, Applying Law of Equilibrium For 12 Kg Block.

Equation will be,

⟼ M₂g - T = M₂a

Substituting the Values,

⟼ 12 x 10 - T = 12 x a

⟼ 120 - T = 12 a

⟼ 120 - T = 12 a ____ [2]

Adding [1] & [2]

⟼ T + 120 - T = 8 a + 80 + 12 a

⟼ 120 = 20 a + 80

⟼ 120 - 80 = 20 a

⟼ 20 a = 120 - 80

⟼ 20 a = 40

⟼ a = 40 / 20

⟼ a = 2 m/s²

⟼ a = 2 m/s².

________________________

________________________

Substituting the value in Equation [1]

⟼ T = 8 a + 80  ___ [1]

Now,

⟼ T = 8 x 2 + 80

⟼ T = 16 + 80

⟼ T = 96 N

⟼ T = 96 N

∴ Tension (T) in the string is 96 N.

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