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Standard XII

Physics

Centripetal Acceleration

If two rodes ...

Question

If two rodes $A$ and $B$ of the same material and length having radii $r_{1}$ and $r_{2}$ respectively are rigidly fixed at one end are twisted by the same couple applied at the other end, then the ratio of
$(\frac{a n g l e o f t w i s t a t t h e e n d o f A}{a n g l e o f t w i s t a t t h e e n d o f B})$ will be

\frac{r_{1}^{2}}{r_{2}^{2}}

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\frac{r_{1}^{3}}{r_{2}^{3}}

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\frac{r_{1}^{4}}{r_{2}^{4}}

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\frac{r_{2}^{4}}{r_{2}^{4}}

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Solution

The correct option is C $\frac{r_{2}^{4}}{r_{2}^{4}}$
By the relation, $C = \frac{π η θ r^{4}}{2 I}$
or $θ \propto \frac{1}{r^{4}}$
So, $θ \propto \frac{1}{r^{4}}$
$\frac{θ_{A}}{θ_{B}} = \frac{r_{2}^{4}}{r_{1}^{4}}$

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If two rodes A and B of the same material and length having radii r1 and r2 respectively are rigidly fixed at one end are twisted by the same couple applied at the other end, then the ratio of(angleoftwistattheendofAangleoftwistattheendofB) will be

The correct option is C r42r42By the relation, C=πηθr42Ior θ∝1r4So, θ∝1r4θAθB=r42r41

The correct option is C $\frac{r_{2}^{4}}{r_{2}^{4}}$
By the relation, $C = \frac{π η θ r^{4}}{2 I}$
or $θ \propto \frac{1}{r^{4}}$
So, $θ \propto \frac{1}{r^{4}}$
$\frac{θ_{A}}{θ_{B}} = \frac{r_{2}^{4}}{r_{1}^{4}}$