Question

Two masses m1 and m2 are connected by a light string passing over a fixed pulley as shown. The system is suspended in a vertical plane. Find the tension in the string connecting m1 and m2 and
acceleration of masses if m1 = 3 kg and m2 = 5 kg. Also find the tension in the rope connecting the centre of pulley to the ceiling
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Answer 1

Answer:

a=2.5 and T=37.5

Explanation:1. M1g-T=M1a

                     2.T-M2g=Ma

dont worry all u need to do is put all the values as given in questions and u will get the answer.

Answer 2

AnSwer :-

As m₂ is heavier, it moves down and m₁ moves up. Let the magnitude of accerlation = a (same for both as they are connected by same string ).

|| Refer fig-1 ||

Let T be the tension in the string.

Draw the force diagrams of the both mass

(i) Net force in the direction of accerlation = m₁a

$\sf T - m_1g = m_1a \: \: \: ....(1)$

(ii) Net force in the direction of accerlation = m₂a

$\sf m_2g - T = m_2a \: \: \: \: ....(2)$

Adding (1) and (2) we get

$\sf m_2g - m_1g = m_1a + m_2a$

$\sf a =\dfrac{m_2 - m_1}{m_2 + m_1}g \: \: \: \: and \: \: \: \: T = \dfrac{2m_1 m_2}{m_2 + m_1}g$

$\sf a =\dfrac{g}{4}= 2.45m/s^2 \: \: \: \: and \: \: \: T = 36.75N$

Free body diagram of pulley

|| Refer fig -2 ||

T$_0$ = tension in the rope tied to the centre of pulley

as pulley is massless, so net force on it is zero.

$\sf T_0 = T + T = 2T$

$\sf T_0 = 2 × 36.75$

$\sf T_0 = 73.5 N$

thus, the tension in the rope connecting the centre of pulley to the ceiling is 73.5N

$\:$

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