Question

Two masses 8kg and 12kg are connected at the two ends of a light inextensible string that goes over a light and frictionless pulley .find acceleration of the masses and the tension in the string when the masses are released?take g=10 .
please give whole solution​

Answer 1

Answer:

Given:

A pulley system has been provided . The pulley is frictionless and the string is inextensible.

To find:

Acceleration of the masses and the tension in the string

Diagram:

Carefully look at the diagram and see the following steps. Also draw the FBD in the copy.

Calculation:

Let tension be T , acceleration be a

For 12 kg mass :

12g - T = 12a........(1)

For 8 kg mass :

T - 8g = 8a ........(2)

Adding the Equations :

∴ 4g = 20a

=> a = g/5 = 10/5 = 2 m/s²

Putting value of "a" in eq.(1)

∴ 12g - T = 12 × 2

=> T = (12 × 10) - 24

=> T = 120 - 24

=> T = 96 N

So final answer :

$\boxed{ \red{acc. = 2 \: m \: {s}^{ - 2}}}$

$\boxed{ \green{tension = 96 \: newtons}}$

Answer 2

Question :

Two masses 8kg and 12kg are connected at the two ends of a light inextensible string that goes over a light and frictionless pulley .find acceleration of the masses and the tension in the string when the masses are released? Take g=10 m/s²

Solution :

From the Question,

• $\sf Mass, M_1 = 12 \ Kg$

• $\sf Mass,M_2 = 8 \ Kg$

• Acceleration due to gravity,g = 10 m/s²

To finD

Acceleration and Tension

Tension acting on an inextensible string is the same in all places

Acceleration of system of masses in an inextensible string is given by

$\boxed{ \boxed{ \tt{a = \dfrac{ {M}_{1} - {M}_{2} }{ {M}_{1} + {M}_{2} } g}}} \\ \\ \longrightarrow \ \sf{a = \dfrac{12 - 8}{12 + 8} \times 10 } \\ \\ \longrightarrow \: \sf{a = \dfrac{40}{20} } \\ \\ \longrightarrow \: \underline{ \boxed{ \sf{a = 2 \: {ms}^{ -2} }}}$

Tension

$\boxed{ \boxed{ \tt{T = \dfrac{2 M_{1} M_{2} }{ M_{1} + M_{2} }g}}} \\ \\ \longrightarrow \: \sf{T = \dfrac{2 \times 12 \times 8}{20} \times 10} \\ \\ \longrightarrow \: \underline{ \boxed{\sf{T = 96 \ N}}}$

Tension in the string is 96 N and the acceleration of the blocks is 2 m/s²