(A) Given: Radius $r = 0.4 \ m$,Angular acceleration $\alpha = 8 \ rad \ s^{-2}$,Mass $m = 4 \ kg$,Acceleration due to gravity $g = 10 \ ms^{-2}$.The

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

(A) Given: Radius $r = 0.4 \ m$,Angular acceleration $\alpha = 8 \ rad \ s^{-2}$,Mass $m = 4 \ kg$,Acceleration due to gravity $g = 10 \ ms^{-2}$.The torque $\tau$ produced by the weight is given by $\tau = mgr$.Also,the torque is related to the moment of inertia $I$ and angular acceleration $\alpha$ by $\tau = I\alpha$.Equating the two expressions for torque:$I\alpha = mgr$$I \times 8 = 4 \times 10 \times 0.4$$I \times 8 = 16$$I = \frac{16}{8} = 2 \ kg \ m^2$.

Class 11 Physics System of Particles and Rotational Motion Relation between Torque and Angular acceleration and it's Application

Medium

$A$ wheel of radius $0.4 \ m$ can rotate freely about its axis as shown in the figure. $A$ string is wrapped around its circumference,and a weight of $4 \ kg$ is suspended from it. Due to the torque,an angular acceleration of $8 \ rad \ s^{-2}$ is produced. The moment of inertia of the wheel is = $...... \ kg \ m^2$ $(g = 10 \ ms^{-2})$

A
$2$
B
$1$
C
$4$
D
$8$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

System of Particles and Rotational Motion

Subtopic

Relation between Torque and Angular acceleration and it's Application

$A$ rod of mass $M$ and length $L$ is placed in a horizontal plane. One of its ends is hinged on a vertical axis. $A$ horizontal force $F = Mg/2$ is applied at a distance of $5L/6$ from the hinged end. What will be the angular acceleration of the rod?

Difficult

View Solution

$A$ rope of negligible mass is wound round a hollow cylinder of mass $3\; kg$ and radius $40\; cm$. What is the angular acceleration of the cylinder if the rope is pulled with a force of $30\; N$? What is the linear acceleration of the rope? Assume that there is no slipping.

Medium

View Solution

Write the Newton's second law for rotational motion about a fixed axis.

Medium

View Solution

The moment of inertia of a wheel about its vertical axis is $2 \ kg \ m^2$. It is rotating about this axis at a speed of $60 \ rpm$. What torque must be applied to bring the wheel to rest in $1 \ minute$?

Difficult

View Solution

$A$ uniform rod of mass $m$ and length $2l$ is balanced on a triangular prism. Now,a length of $l/2$ is cut from one end of the rod and placed over the shortened part such that the ends meet. The initial angular acceleration 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

Similar Questions

$A$ rod of mass $M$ and length $L$ is placed in a horizontal plane. One of its ends is hinged on a vertical axis. $A$ horizontal force $F = Mg/2$ is applied at a distance of $5L/6$ from the hinged end. What will be the angular acceleration of the rod?

$A$ rope of negligible mass is wound round a hollow cylinder of mass $3\; kg$ and radius $40\; cm$. What is the angular acceleration of the cylinder if the rope is pulled with a force of $30\; N$? What is the linear acceleration of the rope? Assume that there is no slipping.

Write the Newton's second law for rotational motion about a fixed axis.

The moment of inertia of a wheel about its vertical axis is $2 \ kg \ m^2$. It is rotating about this axis at a speed of $60 \ rpm$. What torque must be applied to bring the wheel to rest in $1 \ minute$?

$A$ uniform rod of mass $m$ and length $2l$ is balanced on a triangular prism. Now,a length of $l/2$ is cut from one end of the rod and placed over the shortened part such that the ends meet. The initial angular acceleration is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module