Equal torsional torques act on two rods $x{\rm{ }}and{\rm{ }}y$ having equal length. The diameter of rod $y$ is twice the diameter of rod $x.{\mkern 1mu} \,{\mkern 1mu} {\rm{If}}\,\,{\theta _x}{\mkern 1mu} {\mkern 1mu} \,and{\mkern 1mu} \,{\mkern 1mu} {\theta _y}$ are the angles of twist, then $\frac{{{{\rm{\theta }}_x}}}{{{{\rm{\theta }}_y}}} = $

JEE PHYSICS MCQ: MECHANICAL PROPERTIES OF SOLIDS

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Equal torsional torques act on two rods

x\mathrm{ }and\mathrm{ }y

having equal length. The diameter of rod

y

is twice the diameter of rod

x.{\mkern 1mu} \,{\mkern 1mu} \mathrm{If}\,\,{\theta _x}{\mkern 1mu} {\mkern 1mu} \,and{\mkern 1mu} \,{\mkern 1mu} {\theta _y}

are the angles of twist, then

\frac{{{\mathrm{\theta }_x}}}{{{\mathrm{\theta }_y}}} =

View answer and explanation

Correct option: D

Option D (16) is correct because the angle of twist is inversely proportional to the fourth power of the diameter, so doubling the diameter reduces the twist by a factor of 16.

More Questions from MECHANICAL PROPERTIES OF SOLIDS

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A wire is stretched under a force. If the wire suddenly snaps the temperature of the wire The increases in length is

l

of a wire of length

L

by the longitudinal stress. Then the stress is proportional to A steel wire of length

l

and cross sectional area

\mathrm{A}

is stretched by

1 \mathrm{~cm}

under a given load. When the same load is applied to another steel wire of double its length and half of its cross section area, the amount of stretching (extension) is Assertion: From the relation

Y=\frac{F l}{A \Delta l},

we can say that, if length of a wire is doubled, its Young's modulus of elasticity will also becomes two times.

Reason: Modulus of elasticity is a material property. A wire can be broken by applying a load of 200 N. The force required to break another wire of the same length and same material, but double in diameter, is Assertion(A): If radius of cylindrical wire is doubled, then this wire can bear four times stress.

Reason(R): By doubling the radius, area of cross-section will become four times.