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6. system of particles and rotational motion — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics6. system of particles and rotational motion1 Mark
MCQ
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  
  • A
    $0.4\ m$  from mass of $ 0.3\ kg$
  • ✓
    $0.98\ m$  from mass of $0.3\ kg$
  • C
    $0.70\ m$  from mass of $0.7\ kg$
  • D
    $0.98\ m$  from mass of $0.7\ kg$
✓

Answer

Correct option: B.
$0.98\ m$  from mass of $0.3\ kg$
b
$Work-energy$ theorem, $\quad W_{\text {all forces }}=\frac{1}{2} I w^{2}$

Given$:$ $w$ is constant

So required work done to be minimum implies that $I$ must be minimum.

Let the rotational axis passes through O. $I=0.3\left(x^{2}\right)+0.7(1.4-x)^{2}$

For $I$ to be minimum, $\quad \frac{d I}{d x}=0$

$\Longrightarrow 0.3 \times 2(x)-0.7 \times 2(1.4-x)=0$

$\Longrightarrow x=0.98 m$

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