(B) The forces acting on the mass are the tension $T$ in the string and the gravitational force $mg$. The horizontal component of tension provides the

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

(B) The forces acting on the mass are the tension $T$ in the string and the gravitational force $mg$. The horizontal component of tension provides the necessary centripetal force.$T \sin \theta = m \omega^2 R$$T \cos \theta = mg$Dividing the two equations, we get:$\tan \theta = \frac{\omega^2 R}{g}$Given frequency $n = 2/\pi \; \text{rev/sec}$, the angular velocity is $\omega = 2 \pi n = 2 \pi (2/\pi) = 4 \; \text{rad/sec}$.Given radius $R = 1 \; m$ and $g = 10 \; m/s^2$:$\tan \theta = \frac{(4)^2 \times 1}{10} = \frac{16}{10} = \frac{8}{5}$Therefore, $\theta = \tan^{-1} \frac{8}{5}$.

Class 11 Physics 3-2.Motion in Plane Dynamics of circular Motion (Centrifugal force) and Pendulum and Motion on Curved path

Difficult

$A$ body of mass $M = 100 \; g$ is rotating in a horizontal circle with an angular frequency of $n = 2/\pi \; \text{rev/sec}$ as shown in the figure. If the radius of the circular path is $R = 1 \; m$, what is the angle $\theta$ made by the string with the vertical? $(g = 10 \; m/s^2)$

A
$\tan^{-1} \frac{5}{8}$
B
$\tan^{-1} \frac{8}{5}$
C
$\cos^{-1} \frac{8}{5}$
D
$\cos^{-1} \frac{5}{8}$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

3-2.Motion in Plane

Subtopic

Dynamics of circular Motion (Centrifugal force) and Pendulum and Motion on Curved path

$A$ ball of mass $0.5 \ kg$ is attached to a string of length $50 \ cm$. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is $400 \ N$. The maximum possible value of angular velocity of the ball in $rad/s$ is:

DifficultJEE MAIN 2024

View Solution

$A$ train is running at $20 \, m/s$ on a railway line with a radius of curvature of $40,000 \, m$. The distance between the two rails is $1.5 \, m$. For safe running of the train,the elevation of the outer rail over the inner rail is ...... $mm$ $(g = 10 \, m/s^2)$.

Medium

View Solution

$A$ mass is supported on a frictionless horizontal surface. It is attached to a string and rotates about a fixed centre at an angular velocity $\omega_0$. If the length of the string and angular velocity are doubled,the tension in the string which was initially $T_0$ is now

EasyAIIMS 1985

View Solution

When helical gear $M$ turns as shown,gears $I$ & $H$ turn in the following manner. Which of the following is correct? (Assuming no slipping anywhere)

Difficult

View Solution

$A$ tube of length $L$ is filled completely with an incompressible liquid of mass $M$ and closed at both ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity $\omega$. Then the force exerted by the liquid at the other end is

Difficult

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

$A$ body of mass $M = 100 \; g$ is rotating in a horizontal circle with an angular frequency of $n = 2/\pi \; \text{rev/sec}$ as shown in the figure. If the radius of the circular path is $R = 1 \; m$, what is the angle $\theta$ made by the string with the vertical? $(g = 10 \; m/s^2)$

Similar Questions

$A$ ball of mass $0.5 \ kg$ is attached to a string of length $50 \ cm$. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is $400 \ N$. The maximum possible value of angular velocity of the ball in $rad/s$ is:

$A$ train is running at $20 \, m/s$ on a railway line with a radius of curvature of $40,000 \, m$. The distance between the two rails is $1.5 \, m$. For safe running of the train,the elevation of the outer rail over the inner rail is ...... $mm$ $(g = 10 \, m/s^2)$.

$A$ mass is supported on a frictionless horizontal surface. It is attached to a string and rotates about a fixed centre at an angular velocity $\omega_0$. If the length of the string and angular velocity are doubled,the tension in the string which was initially $T_0$ is now

When helical gear $M$ turns as shown,gears $I$ & $H$ turn in the following manner. Which of the following is correct? (Assuming no slipping anywhere)

$A$ tube of length $L$ is filled completely with an incompressible liquid of mass $M$ and closed at both ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity $\omega$. Then the force exerted by the liquid at the other end is

Vedclass Test Series

Exam Paper Generator

Online Exam Module