A mass m suspended at the end of spring of spring constant k and oscillate at periodic time T. If spring is cut into two part of equal length and tow pails are now connected in parallel and a block is suspended at the end of the combined spring and oscillate then find new periodic time.

Options

A. `2T`
B. `T`
C. `(T)/(sqrt(2))`
D. `(T)/(2)`

Answer

D

Explanation

`T propto (1)/(sqrt(k))`
The effective force constant in parallel combination of spring when spring is divided into two equal parts
`k_(2)= 2k+ 2k`
`therefore k_(2)= 4k`
Now, `(T_2)/(T_1)= sqrt((k_1)/(k_2))= sqrt((k)/(4k))= (1)/(2)`
`therefore T_(2)= (T_1)/(2)`.