JEE MAIN - Physics (2016 - 10th April Morning Slot - No. 6)
A thin 1 m long rod has a radius of 5 mm. A force of 50 $$\pi $$kN is applied at one end to determine its Young’s modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is 0.01 mm, which of the following statements is false ?
$${{\Delta \gamma } \over \gamma }$$ gets minimum contribution
from the uncertainty in the length.
The figure of merit is the largest for the length of the rod.
The maximum value of $$\gamma $$ that can be determined is 2 $$ \times $$ 1014 N/m2
$${{\Delta \gamma } \over \gamma }$$ gets its maximum contribution
from the uncertainty in strain
설명
Young's Modulus of the material of the rod is
$$Y = {{Stress} \over {Strain}} = {{(F/A)} \over {(\Delta l/l)}}$$
Here, Y remains maximum, when $$\Delta$$l is of least count.
That is,
$${Y_{\max }} = \left[ {{{50\pi \times {{10}^3}N} \over {\pi {{(5 \times {{10}^{ - 3}})}^2}{m^2}}}} \right]\left[ {{{1m} \over {0.01 \times {{10}^{ - 3}}m}}} \right]$$
$$ = 2 \times {10^4}N/{m^2}$$