Question

A mass M suspended from a light spring which is fixed at the upper end to rigid support oscillates in a vertical line with a period of 2 s. If the mass is increased by 20 g, then the time period of oscillation increases by 1 s. The value of M is ______. 

पर्याय

• 1g

• 2g

• 16g

• 24g

Answer 1

A mass M suspended from a light spring which is fixed at the upper end to rigid support oscillates in a vertical line with a period of 2 s. If the mass is increased by 20 g, then the time period of oscillation increases by 1 s. The value of M is 16g. 

Explanation:

The time period of oscillations is given by,

T = `2π sqrt("M"/"k")`

where k is the force constant of the spring

∴ 2 = `2π sqrt("M"/"k")`  .......(i)

When the mass is increased,

3 = `2π sqrt(("M" + 20)/"k")`  .......(ii)

Dividing equation (ii) by equation (i), we get,

`3/2 = 2π sqrt(("M" + 20)/"k")`

Squaring both sides,

`9/4 = ("M" + 20)/"M"` or 9M = 4M + 80

∴ 5M = 80

∴ M = 16g