Question

consider the arrangement shown where two blocks are connected by a uniform rope of mass 4 kg. The arrangement is lifted up vertically by a vertical upward force of 150 N magnitude.The ration of tension in the rope at A to B would be

Answer 1

Given:

Consider the arrangement shown where two blocks are connected by a uniform rope of mass 4 kg. The arrangement is lifted up vertically by a vertical upward force of 150 N magnitude.

To find:

Ratio of tension at A and B:

Calculation:

[Point A actually means the top of the rope and point B means the bottom of the rope]

For the 4 kg block:

$\therefore \: T_{B} - 4g = 4a$

$\implies \: T_{B} = 4a + 4g$

$\implies \: T_{B} = 4(a + g) \: \: \: .....(1)$

For the 4 kg rope and 4kg block:

$\therefore \: T_{A} - (4 + 4)g = (4 + 4)a$

$\implies \: T_{A} - 8g = 8a$

$\implies \: T_{A} = 8a + 8g$

$\implies \: T_{A} = 8(a + g) \: \: \: \: .....(2)$

So, required ratio:

$\therefore \: T_{A} : T_{B} = 8(a + g) : 4(a + g)$

$\implies \: T_{A} : T_{B} = 8: 4$

$\implies \: T_{A} : T_{B} = 2 : 1$

So, final answer is:

$\boxed{ \bold{ \: T_{A} : T_{B} = 2 : 1}}$