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

Byju's Answer

Standard XII

Physics

Vector Component

Two point mas...

Question

Two point masses of $0.3 k g$ and $0.7 k g$ are fixed at the ends of a rod of length $1.4 m$ and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum is located at a distance of

0.42 m

from the mass of

0.3 k g

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

0.70 m

from the mass of

0.7 k g

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

0.98 m

from the mass of

0.3 k g

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

0.98 m

from the mass of

0.7 k g

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

Open in App

Solution

The correct option is C $0.98 m$ from the mass of $0.3 k g$
Work-energy theorem, $W_{a l l f o r c e s} = \frac{1}{2} I w^{2}$
Given: $w$ is constant
So required work done to be minimum implies that $I$ must be minimum.
Let the rotational axis passes through O.
$I = 0.3 (x^{2}) + 0.7 (1.4 - x)^{2}$
For $I$ to be minimum, $\frac{d I}{d x} = 0$
$⟹ 0.3 \times 2 (x) - 0.7 \times 2 (1.4 - x) = 0$
$⟹ x = 0.98 m$

Suggest Corrections

Similar questions

Q. Two point masses of 0.3 kg and 0.7 kg are fixed at the ends of a rod of length 1.4 m and of negligible mass.
The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the
rod through which the axis should pass in order that the work required for rotation of the rod is minimum, is
located at a distance of

Q. A rod of length

1.4 m

and negligible mass has two masses of

0.3 k g

and

0.7 k g

tied to its two ends. Find the location of the point on this rod where the rotational energy is minimum where the rod is rotated about that point.

Q. A thin rod of negligible mass and length 1.4 m has two point masses of 0.3. kg and 0.7 kg are fixed at its ends.
The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. In order that the work required for rotation of the rod be minimum, the point on the rod through which the axis should pass, is located from the 0.3 kg mass at a distance of

Two point masses A of mass M and B of mass 4M are fixed at the ends of a rod of length l and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The work required for rotating the rod will be minimum when the distance of axis of rotation from the mass A is at

Q. Point masses

m_{1}

and

m_{2}

are placed at the opposite ends of a rigid rod of length L, and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point P on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity

ω_{0}

is minimum, is given by:

Join BYJU'S Learning Program