Question

A body of mass 5 g is in S.H.M. about a point with amplitude 10 cm. Its maximum velocity is 100 cm/s. Its velocity will be 50 cm/s at a distance of, ____________.

Options

• 5 cm

• `5 sqrt2  "cm"`

• `5 sqrt3  "cm"`

• `10 sqrt2  "cm"`

Answer 1

A body of mass 5 g is in S.H.M. about a point with amplitude 10 cm. Its maximum velocity is 100 cm/s. Its velocity will be 50 cm/s at a distance of, `5 sqrt3  "cm"`.

Explanation:

`"m" = 5"g";  "A" = 10  "cm"`

`"v"_max = 100  "cm/s"`

`"v" = 50  "cm/s"`

`"v"_"max" = omega "A"`

`100 = omega xx 10`

`therefore omega = 10  "rad/s"`

`"v" = omega^2 ("A"^2 - "x"^2)`

`(50)^2 = (10)^2 (10^2 - "x"^2)`

`25 = 10^2 - "x"^2`

`therefore "x"^2 = 10 - 25 = 75`

`therefore "x" = 5sqrt3  "cm"`