An iron tyre is to be fitted onto a wooden wh | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Initial diameter of the wheel $D_w = 1000 \, mm$.Initial diameter of the tyre $D_t = 1000 - 6 = 994 \, mm$.Initial radius of the tyre $R = 497 \,

Vedclass · Accepted Answer

$500$

Vedclass · Answer

(C) Initial diameter of the wheel $D_w = 1000 \, mm$.Initial diameter of the tyre $D_t = 1000 - 6 = 994 \, mm$.Initial radius of the tyre $R = 497 \, mm$.Change in radius required $\Delta R = 3 \, mm$.The coefficient of linear expansion $\alpha$ is related to the coefficient of cubical expansion $\gamma$ by $\alpha = \frac{\gamma}{3}$.Given $\gamma = 3.6 	imes 10^{-5} \, ^oC^{-1}$,so $\alpha = \frac{3.6 	imes 10^{-5}}{3} = 1.2 	imes 10^{-5} \, ^oC^{-1}$.The change in circumference $\Delta L$ is given by $\Delta L = 2\pi \Delta R = L \alpha \Delta 	heta = (2\pi R) \alpha \Delta 	heta$.Thus,$\Delta R = R \alpha \Delta 	heta$.$\Delta 	heta = \frac{\Delta R}{R \alpha} = \frac{3}{497 	imes 1.2 	imes 10^{-5}} \approx \frac{3}{0.005964} \approx 503 \, ^oC$.Rounding to the nearest provided option,the required temperature increase is $500 \, ^oC$.

Similar Questions

$A$ hole is drilled in a copper sheet. The diameter of the hole is $4.24 \,cm$ at $27.0^{\circ} C$. What is the diameter of the hole when it is heated to $35^{\circ} C$?

$A$ metal rod having a coefficient of linear expansion $2 \times 10^{-5} /{ }^{\circ} C$ is $0.75 \ m$ long at $45^{\circ} C$. When the temperature rises to $65^{\circ} C$,the increase in length of the rod will be: (in $mm$)

$A$ pendulum clock loses $12\;s$ a day if the temperature is $40^{\circ}C$ and gains $4\;s$ a day if the temperature is $20^{\circ}C$. The temperature at which the clock will show correct time,and the coefficient of linear expansion $(\alpha)$ of the metal of the pendulum shaft are respectively:

The difference in length between an iron rod and a copper rod is $10 \ cm$ at all temperatures. If ${\alpha _{Fe}} = 11 \times {10^{ - 6}} \, ^\circ C^{ - 1}$ and ${\alpha _{Cu}} = 17 \times {10^{ - 6}} \, ^\circ C^{ - 1}$,what are their lengths respectively?

Vedclass Test Series

Exam Paper Generator

Online Exam Module