A simple pendulum of length L carries a bob of mass m. When the bob is at its lowest position, it is given that the minimum horizontal speed necessary for it to move in a vertical circle about the point of suspension. When the string is horizontal, the net force on the bob is

Question

A simple pendulum of length L carries a bob of mass m. When the bob is at its lowest position, it is given that the minimum horizontal speed necessary for it to move in a vertical circle about the point of suspension. When the string is horizontal, the net force on the bob is (A) √10 mg (B) √5 mg (C) 4 mg (D) 1 mg

Tardigrade Admin · Accepted Answer

According to the question, the bob is moving in a vertical circle, so the velocity at lowest point

v = 5 r g

Now, applying conservation of mechanical energy, we get

\frac{1}{2} m \times 5 r g = \frac{1}{2} m v^{2} + m g r

or,

\frac{5}{2} r g = \frac{v ^{2}}{2} + r g

or,

\frac{3}{2} r g = \frac{v ^{2}}{2}

or,

v^{2} = 3 r g ... (i)

Now, Horizontal force on the bob,

F x = F_{c} = \frac{m v ^{2}}{r}

= \frac{m \times 3 r g}{r} = 3 m g

[from Eq. (i)]
Vertical force on the bob,

F_{y} = m g

∴ F_{net} = F_{x}^{2} + F_{y}^{2}

= (3 m g)^{2} + (m g)^{2} = 10 m g

Q. A simple pendulum of length $L$ carries a bob of mass $m$ . When the bob is at its lowest position, it is given that the minimum horizontal speed necessary for it to move in a vertical circle about the point of suspension. When the string is horizontal, the net force on the bob is

$10 m g$

$5 m g$

$4 m g$

$1 m g$

Q. A simple pendulum of length L carries a bob of mass m. When the bob is at its lowest position, it is given that the minimum horizontal speed necessary for it to move in a vertical circle about the point of suspension. When the string is horizontal, the net force on the bob is

10​mg

5​mg

4mg

1mg

Q. A simple pendulum of length $L$ carries a bob of mass $m$ . When the bob is at its lowest position, it is given that the minimum horizontal speed necessary for it to move in a vertical circle about the point of suspension. When the string is horizontal, the net force on the bob is

$10 m g$

$5 m g$

$4 m g$

$1 m g$