If one string be cut, the tension of each of the other two strings will be changed in the ratio (i.e. the ratio of final tension after cutting the string to tension before cutting the string):

Question

TestHub · Accepted Answer

When one string is cut, the particle hangs from two strings of length $a$ attached at points $2 b$ apart; it settles in the vertical plane through the two attachment points, directly below their midpoint, so each string makes an angle $θ'$ with the vertical where

$cos θ' = \frac{a ^{2} - b ^{2}}{a}$

and vertical equilibrium gives

$2 T_{f} cos θ' = m g \Rightarrow T_{f} = \frac{m g a}{2 a ^{2} - b ^{2}}$

The ratio of the final to the initial tension is therefore

$\frac{T _{f}}{T _{i}} = \frac{3 cos θ}{2 cos θ '} = \frac{3 3 a ^{2} - 4 b ^{2}}{2 a ^{2} - b ^{2}}$

Corrected option (A) matches the derived ratio. The printed option (A) omitted radical signs; they have been restored above.

Physics - NLM Question with Solution | TestHub

Options:

Doubts & Discussion