Three rods of equal length l are joined to fo | vedclass

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

Question

(D) In the right-angled triangle $POR,$ the distance $OR$ is given by:$(OR)^2 = (PR)^2 - (PO)^2 = l^2 - (l/2)^2 = 3l^2/4.$When the temperature increas

Vedclass · Accepted Answer

$\alpha_1 = 4\alpha_2$

Vedclass · Answer

(D) In the right-angled triangle $POR,$ the distance $OR$ is given by:$(OR)^2 = (PR)^2 - (PO)^2 = l^2 - (l/2)^2 = 3l^2/4.$When the temperature increases by $\Delta t,$ the lengths change as $l' = l(1 + \alpha \Delta t).$Since $OR$ remains constant,$(OR)^2$ must remain constant:$(OR)^2 = (PR')^2 - (PO')^2$$3l^2/4 = [l(1 + \alpha_2 \Delta t)]^2 - [l/2(1 + \alpha_1 \Delta t)]^2$Expanding the terms and neglecting higher-order terms like $(\Delta t)^2$:$3l^2/4 = l^2(1 + 2\alpha_2 \Delta t) - (l^2/4)(1 + 2\alpha_1 \Delta t)$$3l^2/4 = l^2 + 2l^2\alpha_2 \Delta t - l^2/4 - (l^2/4)(2\alpha_1 \Delta t)$$3l^2/4 = 3l^2/4 + 2l^2\alpha_2 \Delta t - (l^2/2)\alpha_1 \Delta t$Setting the change to zero:$0 = 2l^2\alpha_2 \Delta t - (l^2/2)\alpha_1 \Delta t$$2\alpha_2 = \alpha_1/2$$\alpha_1 = 4\alpha_2$

Similar Questions

$A$ wire elongates by $l \, mm$ when a load $W$ is hanged from it. If the wire goes over a pulley and two weights $W$ each are hung at the two ends,the elongation of the wire will be (in $mm$):

When a capacitor is connected in series to an $LR$ circuit,the alternating current flowing in the circuit

The value of $\sqrt{42+\sqrt{42+\sqrt{42+\ldots}}}$ is equal to:

Which of the following will not show geometrical isomerism?

The concept of chemical evolution is based on

Vedclass Test Series

Exam Paper Generator

Online Exam Module