(B) The work done to rotate a body with constant angular velocity $\omega$ is given by $W = \frac{1}{2} I \omega^2$. For the work to be minimum,the mo

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

$0.98 \, m$ from the $0.3 \, kg$ mass

(B) The work done to rotate a body with constant angular velocity $\omega$ is given by $W = \frac{1}{2} I \omega^2$. For the work to be minimum,the moment of inertia $I$ of the system must be minimum.Let the axis of rotation be at a distance $x$ from the $0.3 \, kg$ mass. Then the distance from the $0.7 \, kg$ mass is $(1.4 - x)$.The moment of inertia $I$ is given by: $I = m_1 x^2 + m_2 (L - x)^2 = 0.3 x^2 + 0.7 (1.4 - x)^2$.To find the minimum $I$,we differentiate with respect to $x$ and set it to zero:$\frac{dI}{dx} = 0.3(2x) + 0.7(2)(1.4 - x)(-1) = 0$$0.6x - 1.4(1.4 - x) = 0$$0.6x - 1.96 + 1.4x = 0$$2.0x = 1.96$$x = 0.98 \, m$.Thus,the axis should pass at a distance of $0.98 \, m$ from the $0.3 \, kg$ mass.

Class 11 Physics System of Particles and Rotational Motion Mix Example - System of Particles and Rotational Motion

Difficult

Two masses of $0.3 \, kg$ and $0.7 \, kg$ are attached to the ends of a rod of length $1.4 \, m$ and negligible mass. The rod is rotated about an axis perpendicular to its length with a constant angular speed. The point on the rod through which the axis should pass so that the work required to rotate the rod is minimum is:

A
$0.4 \, m$ from the $0.3 \, kg$ mass
B
$0.98 \, m$ from the $0.3 \, kg$ mass
C
$0.70 \, m$ from the $0.7 \, kg$ mass
D
$0.98 \, m$ from the $0.7 \, kg$ mass

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

System of Particles and Rotational Motion

Subtopic

Mix Example - System of Particles and Rotational Motion

State whether the following statements are True or False:
$(1)$ Angular position $\theta$ is a scalar,while angular displacement $\Delta \theta$ is a vector.
$(2)$ The relation between linear velocity $\vec{v}$ and angular velocity $\vec{\omega}$ for a particle in rotational motion is given by $\vec{v} = \vec{r} \times \vec{\omega}$.
$(3)$ The moment of inertia of a rigid body is constant.
$(4)$ The moment of momentum is called angular momentum.

Medium

View Solution

Two flywheels are connected by a non-slipping belt as shown in the figure. $I_1 = 4 \ kg \ m^2$,$r_1 = 20 \ cm$,$I_2 = 20 \ kg \ m^2$,and $r_2 = 30 \ cm$. $A$ torque of $10 \ Nm$ is applied on the smaller wheel. Match the entries of column $I$ with appropriate entries of column $II$.
Quantities Their numerical values (in $SI$ units)
a. Angular acceleration of smaller wheel $1$. $5/3$
b. Torque on the larger wheel $2$. $100/3$
c. Angular acceleration of larger wheel $3$. $5/2$

MediumKCET 2025

View Solution

On a solid sphere lying on a horizontal surface,a force $F$ is applied at a height of $R/2$ from the centre of mass. The initial acceleration of a point at the top of the sphere is (there is no slipping at any point).

View Solution

Find the increase in the moment of inertia $I$ of a uniform rod (coefficient of linear expansion $\alpha$) about its perpendicular bisector when its temperature is slightly increased by $\Delta T$.

Medium

View Solution

$A$ thin uniform rod of length $l$ and mass $m$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $\omega$. Its centre of mass rises to a maximum height of:

MediumAIEEE 2009

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

Quantities	Their numerical values (in $SI$ units)
a. Angular acceleration of smaller wheel	$1$. $5/3$
b. Torque on the larger wheel	$2$. $100/3$
c. Angular acceleration of larger wheel	$3$. $5/2$

Similar Questions

On a solid sphere lying on a horizontal surface,a force $F$ is applied at a height of $R/2$ from the centre of mass. The initial acceleration of a point at the top of the sphere is (there is no slipping at any point).

Find the increase in the moment of inertia $I$ of a uniform rod (coefficient of linear expansion $\alpha$) about its perpendicular bisector when its temperature is slightly increased by $\Delta T$.

$A$ thin uniform rod of length $l$ and mass $m$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $\omega$. Its centre of mass rises to a maximum height of:

Vedclass Test Series

Exam Paper Generator

Online Exam Module