Two blocks of mass 2.9 kg and 1.9 kg are suspended from a rigid support S by two inextensible wires each of length 1 meter, see fig. The upper wire has negligible mass and the lower wire has a uniform mass of `0.2kg//m`. The whole system of blocks wires and support have an upward acceleration of `0.2m//s^2`. Acceleration due to gravity is `9.8m//s^2`.

(i) Find the tension at the mid-point of the lower wire.
(ii) Find the tension at the mid-point of the upper wire.

Answer

B

Explanation

Let `lambda` be the mass per unit length of lower wire.
Let us consider the dotted portion as a system and the tension T accelerates the system upwards
`:.` `T=(m_1+lambda l)g=(m_1+lambda l)a`
`:.` `T=(m_1+lambda l)(a+g)`
`=(1.9+0.2xx0.5)(9.8+0.2)=2xx10=20N`
`To find tension `T^'` Let us consider the dotted portion given in figure(2)

`T^'-(m_2g+lambdaxx2lg+m_1g)=(m_1+lambda2l+m_2)a`
`:.` `T^'=(m_1+lambda2l+m_2)(a+g)`
`=(1.9+0.2xx1+2.9)(10)=5xx10=50N`.
Alternatively considering `m_1`, `m_2` and lower wire as a system `T^'-5g=5a`