Two weights w, and w, are attached to the ends of a string which passes over a frictionless pulley. If the pulley is placed in a lift rising up with an acceleration equal to that of gravity i.e. '8', the tension in the string :

Options

A. `(4w_(1)w_(2))/(w_(1)+w_(2))`
B. `(2w_(1)w_(2))/(w_(1)+w_(2))`
C. `(w_(1)w_(2))/(2(w_(1)+w_(2))`
D. `(w_(1)w_(2))/(w_(1)+w_(2))`

Answer

a

Explanation

When the lift is stationary, then `T=(m_(1)m_(2)g)/(m_(1)g+m_(2))=(2W_(1)W_(2))/(W_(1)+W_(2))`
When the pulley is accelerated upward with acceleration g then each of the weight is doubled as
W.= m (g +a) = 2 mg = 2W
`:.T=(2(2W_(1))+(2W_(2)))/(2W_(1)+2W_(2))=(4W_(1)W_(2))/(W_(1)+W_(2))`
Hence correct choice is (a)