MCQ
A wire extends by $1 mm$ when a force is applied. Double the force is applied to another wire of same material and length but half the radius of cross-section. The elongation of the wire in mm will be ........
- ✓$8$
- B$4$
- C$2$
- D$1$
✓
Answer
Correct option: A.
$8$
a
(a)$l = \frac{{FL}}{{\pi {r^2}r}}$==> $l \propto \frac{F}{{{r^2}}}$ (Y and L are constant)
$\frac{{{l_2}}}{{{l_1}}} = \frac{{{F_2}}}{{{F_1}}} \times {\left( {\frac{{{r_1}}}{{{r_2}}}} \right)^2} = 2 \times {(2)^2} = 8$
${l_2} = 8{l_1} = 8 \times 1 = 8mm$
(a)$l = \frac{{FL}}{{\pi {r^2}r}}$==> $l \propto \frac{F}{{{r^2}}}$ (Y and L are constant)
$\frac{{{l_2}}}{{{l_1}}} = \frac{{{F_2}}}{{{F_1}}} \times {\left( {\frac{{{r_1}}}{{{r_2}}}} \right)^2} = 2 \times {(2)^2} = 8$
${l_2} = 8{l_1} = 8 \times 1 = 8mm$
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
A sounding body of negligible dimension emitting a frequency of $150\,\, Hz$ is dropped from a height. During its fall under gravity it passes near a balloon moving up with a constant velocity of $2m/s$ one second after it started to fall.The difference in the frequency observed by the man in balloon just before and just after crossing the body will be : (Given that -velocity of sound $= 300m/s; g = 10m/s^2$)
→A force of $10$ Newton acts on a body of mass $20kg$ for $10 \,seconds$. Change in its momentum is ........... $kg\,m/s$
→Which of the prism is used to see infra-red spectrum of light
Two forces of $12 \,N$ and $8 \,N$ act upon a body. The resultant force on the body has maximum value of........$N$
→A body projected along a frictionless inclined plane of angle of inclination $30^o$ covers a distance of $40\, m$ along the plane. If the body is projected with the same speed at angle of $30^o$ with the ground, it will have a range of : (Take $g = 10\, m/s^2$)
→The equation of motion of a projectile are given by $ x = 36 t\,metre$ and $2y = 96 t -9.8 t^2\, metre$. The angle of projection is
→A Carnot engine takes $6000 \,cal$ of heat from a reservoir at $627^{\circ} C$ and gives it to a sink at $27^{\circ} C$. The work done by the engine is ......... $kcal$
→A glass full of hot milk is poured on the table. It begins to cool gradually. Which of the following is correct?
Three cubic shaped bodies whose masses are $m _1=20$ $kg , m _2=40 kg$ and $m _3=60 kg$ are kept on a frictionless surface as shown in figure. All three bodies are connected by an inextensible string. The values of $T _1$ and $T_2$ will be :
→A particle of mass $m$ moving horizontally with $v_0$ strikes $a$ smooth wedge of mass $M$, as shown in figure. After collision, the ball starts moving up the inclined face of the wedge and rises to $a$ height $h$. Choose the correct statement related to the wedge $M$
→