MCQ
Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is $1: 4,$ the ratio of their diameters is
- A$1: \sqrt{2}$
- B$1: 2$
- C$2:1$
- ✓$\sqrt{2}: 1$
✓
Answer
Correct option: D.
$\sqrt{2}: 1$
d
$\frac{\text { Energystored }}{\text { Volume }}=\frac{1}{2} \frac{(\text { Stress })^{2}}{\mathrm{Y}}$
$\frac{\text { Energystored }}{\text { Volume }}=\frac{1}{2} \frac{(\text { Stress })^{2}}{\mathrm{Y}}$
$\frac{\mathrm{u}_{1}}{\mathrm{u}_{2}}=\frac{1}{4} \Rightarrow 4 \mathrm{u}_{1}=\mathrm{u}_{2}$
$4 \frac{1}{2 \mathrm{Y}}\left[\frac{\mathrm{W} \cdot 4}{\pi \mathrm{d}_{1}^{2}}\right]^{2}=\frac{1}{2 \mathrm{Y}}\left[\frac{\mathrm{W} \cdot 4}{\pi \mathrm{d}_{2}^{2}}\right]^{2}$
$4=\left(\frac{\mathrm{d}_{1}}{\mathrm{d}_{2}}\right)^{4}$
$\Rightarrow \frac{\mathrm{d}_{1}}{\mathrm{d}_{2}}=\sqrt{2}: 1$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The unit of self inductance of a coil is
A vibratory motion is represented by $x = 2A\,\cos \omega t + A\,\cos \,\left( {\omega t + \frac{\pi }{2}} \right) + A\,\cos \,\left( {\omega t + \pi } \right)$ $ + \frac{A}{2}\,\cos \left( {\omega t + \frac{{3\pi }}{2}} \right)$. The resultant amplitude of the motion is
→A heavy stone is thrown from a cliff of height $h$ with a speed $v.$ The stone will hit the ground with maximum speed if it is thrown:
→An automobile travelling with a speed of $60\,\,km/h,$ can brake to stop within a distance of $20 \,m$. If the car is going twice as fast, i.e. $120\, km/h$, the stopping distance will be ........... $m$
→A flat horizontal board moves up and down in $SHM$ of amplitude $\alpha$. Then the shortest permissible time period of the vibration such that an object placed on the board may not lose contact with the board is
A mass hangs from a spring and oscillates vertically. The top end of the spring is attached to the top of a box, and the box is placed on a scale, as shown in the figure. The reading on the scale is largest when the mass is
A body weight $500 \,N$ on the surface of the earth. How much would it weigh half way below the surface of the earth ....... $N$
→A circular loop carrying a current is replaced by an equivalent magnetic dipole. A point on the loop is in:
A stone is projected from the ground with velocity $25\,m/s$. Two seconds later, it just clears a wall $5 \,m$ high. The angle of projection of the stone is ........ $^o$ $(g = 10m/{\sec ^2})$
→In summer, a mild wind is often found on the shore of a calm river. This is caused due to,