A simple pendulum is released from rest at th | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(b)

Let $v$ is the velocity of bob at position $	heta$ after being released from horizontal position.

From energy conservation, we have

$m g

Vedclass · Accepted Answer

$\phi=	an ^{-1}\left(\frac{	an 	heta}{2}ight)$

Vedclass · Answer

(b)

Let $v$ is the velocity of bob at position $	heta$ after being released from horizontal position.

From energy conservation, we have

$m g h=\frac{1}{2} m v^2$

$\Rightarrow m g(l \cos 	heta)=\frac{1}{2} m v^2$

$\Rightarrow \quad \frac{v^2}{l}=2 g \cos 	heta \quad \dots(i)$

Restoring force on bob is component of weight.

So, tangential component of acceleration is

$a_t=g \sin 	heta \quad \dots(ii)$

If total acceleration a makes angle $\phi$ with string. Then,

Tangential component,

$a_t=a \sin \phi$

and radial component, $a_c=a \cos \phi$

So, $\quad \frac{a_t}{a_c}=\frac{a \sin \phi}{a \cos \phi}=	an \phi$

$\Rightarrow \quad 	an \phi=\frac{a_i}{a_c} \quad \dots(iii)$

Substituting values of $a_t$ and $a_c$ from Eqs.

$(i)$ and $(ii)$ in Eq. $(iii)$, we get

$	an \phi=\frac{g \sin 	heta}{2 g \cos 	heta}$

$\Rightarrow \quad 	an \phi=\frac{	an 	heta}{2}$

So, $\quad \phi=	an ^{-1}\left(\frac{	an 	heta}{2}ight)$

A simple pendulum is released from rest at the horizontally stretched position. When the string makes an angle $\theta$ with the vertical, the angle $\phi$ which the acceleration vector of the bob makes with the string is given by

Similar Questions

If the time period of a two meter long simple pendulum is $2\, s$, the acceleration due to gravity at the place where pendulum is executing $S.H.M.$ is

A simple pendulum of length $ l$ has a brass bob attached at its lower end. Its period is $T$. If a steel bob of same size, having density $ x$ times that of brass, replaces the brass bob and its length is changed so that period becomes $2T$, then new length is

There is a simple pendulum hanging from the ceiling of a lift. When the lift is stand still, the time period of the pendulum is $T$. If the resultant acceleration becomes $g/4,$ then the new time period of the pendulum is

If two persons sitting on a swing instead of one, why the periodic time does not changed ?

The periodic time of a simple pendulum of length $1\, m $ and amplitude $2 \,cm $ is $5\, seconds$. If the amplitude is made $4\, cm$, its periodic time in seconds will be