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Rotational Motion question

2011 · Q103
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Rotational Motion question

2011 · Q103

NEETPhysicsRotational MotionMCQ+4 / −1
A small mass attached to a string rotates on a frictionless table top as shown. If the tension in the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2, the kinetic energy of the mass will

AIPMT 2011 Mains Physics - Rotational Motion Question 58 English
  1. A
    decrease by a factor of 2
  2. B
    remain constant
  3. C
    increase by a factor of 2
  4. D
    increase by a factor of 4
View written solutionFree

Correct answer: D

According to law of conservation of angular momentum

mvr = mv'r'

vr=v′(r2)vr = v'\left( {{r \over 2}} \right)vr=v′(2r​)

v′=2vv' = 2vv′=2v    ...(i)

∴\therefore∴ KK′=12mv212mv′2=(vv′)2{K \over {K'}} = {{{1 \over 2}m{v^2}} \over {{1 \over 2}mv{'^2}}} = {\left( {{v \over {v'}}} \right)^2}K′K​=21​mv′221​mv2​=(v′v​)2

⇒K′K=(v′v)2=(2)2 \Rightarrow {{K'} \over K} = {\left( {{{v'} \over v}} \right)^2} = {\left( 2 \right)^2}⇒KK′​=(vv′​)2=(2)2    (Using (i))

⇒K′=4K \Rightarrow K' = 4K⇒K′=4K

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