Question

A pendulum has length of 0.4 m and maximum speed 4 m/s. When the length makes an angle 30° with the horizontal, its speed will be ______.
`[sin  pi/6 = cos  pi/3 = 0.5 and "g" = 10 "m"//"s"^2]`

विकल्प

• `2sqrt3` m/s

• `2sqrt2` m/s

• `sqrt3` m/s

• `2sqrt5` m/s

Answer 1

A pendulum has length of 0.4 m and maximum speed 4 m/s. When the length makes an angle 30° with the horizontal, its speed will be `underline(2sqrt3 "m"//"s")`.

Explanation:

h = L - L cos 0 = L(1 - cos θ)

= 0.4 (1 - cos 60°)

`= 0.4 (1 - 1/2)`

`= 0.4 xx 1/2`

= 0.2

`1/2 "mv"_1^2 = 1/2 "mV"_2^2` + mgh

`"V"_1^2 = "V"_2^2 + 2"gh"`

`therefore "V"_2^2 = "V"_1^2 - 2"gh"`

`= (4)^2 - 2 xx 10 xx 0.2`

= 16 - 4 = 12

`therefore "V"_2 = sqrt12 = 2sqrt3`m/s