A spring balance has a scale that reads from 0 to 50kg. The length of the scale is 20cm. A body suspended from this balance, when displaced and released, oscillates with period of 0.6s. What is the weight of the body ?

Explanation

Let the tension in the rope be T and the horizontal acceleration be a.
In the forces acting on the two blocks have been shown. They are at rest relative to A, if
T - `m_(2)g sin beta - m_(2)a cos beta = 0`
T - ` m_(1)g sin alpha + m_(1)a cos alpha = 0`
Subtracting (2) from (1) , we get,
`g(m_(1) sin alpha - m_(2) sin beta) = a(m_(1) cos alpha + m_(2) cos beta)`
or, a = `(m_(1) sin alpha - m_(2) sin beta)/(m_(1) cos alpha + m_(2) cos beta ) xx g`
`therefore" " T = m_(2) a cos beta + m_(2)g sin beta`
` = m_(2) g [ (m_(1) sin alpha - m_(2) sin beta)/(m_(1) cos alpha + m_(2) cos beta )cdot cos beta + sin beta ] `
`= (m_(1) m_(2) sin(alpha + beta))/(m_(1) cos alpha + m_(2) cos beta) g`.