A small sphere of mass m is connected by a string to a nail at O and moves in a circle of radius r on the smooth plane inclined at an angle of - with the horizontal- If the sphere moves with minimum velocity at A such that string does not get slack- then what will be the tension in the string when it passes through point C-

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Friction and Vertical Circular Motion Problems

A small spher...

Question

A small sphere of mass $m$ is connected by a string to a nail at $O$ and moves in a circle of radius $r$ on the smooth plane inclined at an angle of $θ$ with the horizontal. If the sphere moves with minimum velocity at A such that string does not get slack, then what will be the tension in the string when it passes through point C?

\frac{10 m g}{5}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{18 m g}{5}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{9 m g}{5}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{11 m g}{5}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $\frac{18 m g}{5}$
The situation can be considered as similar to vertical circular motion in which effective acceleration due to gravity can be taken as $g sin (37 °)$ in place of $g$ .
Similarly, from concept of vertical circular motion, minimum velocity at A should be
$v_{A} = \sqrt{g sin 37 ° r} = \sqrt{\frac{3}{5} g r}$
To find velocity at C, using concept of vertical circular motion

$\Rightarrow v_{c} = \sqrt{5 g r sin (37 °)} = \sqrt{g r (5 \times \frac{3}{5})} = \sqrt{3 g r}$
$T_{c} - m g sin 37^{\circ} = \frac{m {v_{c}}_{c}^{2}}{r}$
⇒ $T_{c} = 3 m g + \frac{3 m g}{5} = \frac{18}{5} m g$

Suggest Corrections

Similar questions

Q. A small sphere of mass

m

is connected by a string to a nail at

O

and moves in a circle of radius

r

in the smooth plane include at an angle

θ

with the horizontal. If the sphere has a velocity

u

at the top position

A

. Mark the correct options.

Q. A mass

m

moves in a circle on a smooth horizontal plane with velocity

v_{0}

at a radius

R_{0}

. The mass is attached to a string which passes through a smooth hole in the plane as shown.

The tension in the string is increased gradually and finally

m

moves in a
circle of radius

R_{0} / 2

. Then, the final value of the kinetic energy of particle is

Q. A mass,

m

, moves in a circle on a smooth horizontal plane with velocity,

V_{0}

, at a radius,

R_{0}

. The mass is attached to a string which passes through a smooth hole in the plane as shown. The tension in the string is increased gradually and finally

m

moves in a circle of radius

\frac{R_{0}}{2}

. The final value of the kinetic energy is

Q. A mass

m

moves in a circle on a smooth horizontal plane with velocity

v_{0}

at a radius

R_{0}

. The mass is attached to a string which passes through a smooth hole in the plane as shown.

The tension in the string is increased gradually and finally

m

moves in a
circle of radius

R_{0} / 2

. Then, the final value of the kinetic energy of particle is

A mass m moves in a circle on a smooth horizontal plane with velocity v₀ at a radius R₀. The mass is attached to a string which passes through a smooth hole in the plane as shown.

The tension in the string is increased gradually and finally m moves in a circle of radius $\frac{R_{0}}{2}$ . The final value of the kinetic energy is :

Join BYJU'S Learning Program