A bucket of water is being revolved in vertical circle of radius 1 m. Minimum frequency required to prevent the water from getting down the path is (g=10 m/s2)

Question

A bucket of water is being revolved in vertical circle of radius 1 m. Minimum frequency required to prevent the water from getting down the path is (g=10 m/s2)  (A)  (2π /√10)  (B)  (2π /√5)  (C)  (√10/2π )  (D)  (√5/2π )

Tardigrade Admin · Accepted Answer

As radius is doubled hence, force will be halved. v min =r ω min v min =r × 2 π n min n min =(v min /2 π r)=(√r g/2 π r) ∴ n min =(√1 × 10/2 π × 1)=(√10/2 π)

Q. A bucket of water is being revolved in vertical circle of radius $1 m$ . Minimum frequency required to prevent the water from getting down the path is $(g = 10 m / s^{2})$

$\frac{2 π}{10}$

$\frac{2 π}{5}$

$\frac{10}{2 π}$

$\frac{5}{2 π}$

As radius is doubled hence, force will be halved.
$v_{m i n} = r ω_{m i n}$
$v_{m i n} = r \times 2 π n_{m i n}$
$n_{m i n} = \frac{v _{m i n}}{2 π r} = \frac{r g}{2 π r}$
$∴ n_{m i n} = \frac{1 \times 10}{2 π \times 1} = \frac{10}{2 π}$

Q. A bucket of water is being revolved in vertical circle of radius 1m. Minimum frequency required to prevent the water from getting down the path is (g=10m/s2)

10​2π​

5​2π​

2π10​​

2π5​​