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Rotational Motion question

2013 · Q149
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Rotational Motion question

2013 · Q149

NEETPhysicsRotational MotionMCQ+4 / −1
A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in figure. When string is cut, the initial angular acceleration of the rod is

NEET 2013 Physics - Rotational Motion Question 70 English
  1. A
    2gL{{2g} \over L}L2g​
  2. B
    2g2L{{2g} \over {2L}}2L2g​
  3. C
    3g2L{{3g} \over {2L}}2L3g​
  4. D
    gL{g \over L}Lg​
View written solutionFree

Correct answer: C

NEET 2013 Physics - Rotational Motion Question 70 English Explanation

When the string is cut, the rod will rotate about P. Let α\alpha α be initial angular acceleration of the rod.Then

Torque, τ=Iα=ML23α\tau = I\alpha = {{M{L^2}} \over 3}\alpha τ=Iα=3ML2​α      ...(i)

(Moment of inertia of the rod about one end = ML23{{M{L^2}} \over 3}3ML2​)

Also, τ=MgL2\tau = Mg{L \over 2}τ=Mg2L​ ...(ii)

Equating (i) and (ii), we get

MgL2=ML23α⇒α=3g2LMg{L \over 2} = {{M{L^2}} \over 3}\alpha \Rightarrow \alpha = {{3g} \over {2L}}Mg2L​=3ML2​α⇒α=2L3g​

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