(C) The initial centripetal force is given by $F_1 = \frac{mv^2}{r}$.After a $20 \%$ increase,the new values are $m' = 1.2m$,$v' = 1.2v$,and $r' = 1.2

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(C) The initial centripetal force is given by $F_1 = \frac{mv^2}{r}$.After a $20 \%$ increase,the new values are $m' = 1.2m$,$v' = 1.2v$,and $r' = 1.2r$.The new force $F_2$ required is:$F_2 = \frac{m' (v')^2}{r'} = \frac{(1.2m)(1.2v)^2}{1.2r}$$F_2 = \frac{1.2m \times 1.44v^2}{1.2r} = 1.44 \frac{mv^2}{r} = 1.44 F_1$.The change in force is $\Delta F = F_2 - F_1 = 1.44 F_1 - F_1 = 0.44 F_1$.The percentage change is $\frac{\Delta F}{F_1} \times 100 = 0.44 \times 100 = 44 \%$.Therefore,the force must be increased by $44 \%$.

Class 11 Physics 3-2.Motion in Plane Mix Examples-Motion in Plane

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$A$ particle of mass $m$ performs uniform circular motion of radius $r$ with linear speed $v$ under the application of force $F$. If $m$,$v$,and $r$ are all increased by $20 \%$,the necessary change in force required to maintain the particle in uniform circular motion is: (in $\%$)

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A
$12$
B
$14$
C
$44$
D
$144$

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$A$ particle of mass $m$ performs uniform circular motion of radius $r$ with linear speed $v$ under the application of force $F$. If $m$,$v$,and $r$ are all increased by $20 \%$,the necessary change in force required to maintain the particle in uniform circular motion is: (in $\%$)

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