Two wires A and B of same length and of the same material have th… - Vidyadip

MCQ

Two wires $A$ and $B $ of same length and of the same material have the respective radii ${r_1}$ and ${r_2}$. Their one end is fixed with a rigid support, and at the other end equal twisting couple is applied. Then the ratio of the angle of twist at the end of $A$ and the angle of twist at the end of $B $ will be

A
$\frac{{r_1^2}}{{r_2^2}}$
B
$\frac{{r_2^2}}{{r_1^2}}$
✓
$\frac{{r_2^4}}{{r_1^4}}$
D
$\frac{{r_1^4}}{{r_2^4}}$

✓

Answer

Correct option: C.

$\frac{{r_2^4}}{{r_1^4}}$

c
(c)Twisting couple $C = \frac{{\pi \eta {r^4}\theta }}{{2l}}$

If material and length of the wires $A$ and $B$ are equal and equal twisting couple are applied then

$\theta \propto \frac{1}{{{r^4}}}$ $\Rightarrow $ $\frac{{{\theta _1}}}{{{\theta _2}}} = {\left( {\frac{{{r_2}}}{{{r_1}}}} \right)^4}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 8. mechanical properties of solids→8. mechanical properties of solids — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Two particle $P$ and $Q$ are initially $40m$ apart $P$ behind $Q$. Particle $P$ starts moving with a uniform velocity $10m/ s$ towards $Q.$ Particle $Q$ starting from rest has an acceleration $2ms^2$ in the direction of velocity of $P.$ Then the minimum distance between $P$ and $Q$ will be:

The mass of the moon is about $1.2\%$ of the mass of the earth. Compared to the gravitational force the earth exerts on the moon, the gravitational force the moon exerts on earth

When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed $v,$ he sees that rain drops are coming at an angle $60^{\circ}$ from the horizontal. On further increasing the speed of the car to $(1+\beta) v ,$ this angle changes to $45^{\circ} .$ The value of $\beta$ is close to$......$

A boat of mass $90\ kg$ is floating in still water. A boy of mass $30\ kg$ walks from the stem to the bow. The length of the boat is $3\ m$ . Distance through which the boat recoils is .......... $m$

A steel plate of face area $1 \,cm ^2$ and thickness $4 \,cm$ is fixed rigidly at the lower surface. A tangential force $F=10 \,kN$ is applied on the upper surface as shown in the figure. The lateral displacement $x$ of upper surface w.r.t. the lower surface is .............. $m$ (Modulus of rigidity for steel is $8 \times 10^{11} \,N / m ^2$ )

The average $K.E.$ of a gas molecule at $25^\circ C$ is $6.21 \times 10^{-21}J$. Its average $K.E$. at $227^\circ$ will be:

A resonating column has resonant frequencies as $100Hz, 300Hz, 500Hz.$ Then it may:

The equation of $SHM$ is given as:

$x = 3\,sin\, 20\pi t + 4\, cos\, 20\pi t$ ,

where $x$ is in $cms$ and $t$ is in $seconds$ . The amplitude is ..... $cm$

The maximum value attained by the tension in the string of a swinging pendulum is four times the minimum value it attains. There is no slack in the string. The angular amplitude of the pendulum is

$A$ thin uniform straight rod of mass $2\, kg$ and length $1\, m$ is free to rotate about its upper end when at rest. It receives an impulsive blow of $10\, Ns$ at its lowest point, normal to its length as shown in figure. The kinetic energy of rod just after impact is ........ $J$