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Question

All the edges of a block with parallel faces are unequal. Its longest edge is twice its shortest edge. The ratio of the maximum to minimum resistance between parallel faces is


A
2
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B
4
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C
8
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D
indeterminate unless the length of the third edge is specified
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Solution

The correct option is B 4
Let the edges be $$2l, a$$ and $$l$$ in decreasing order.
We know that resistance, $$R=\dfrac{\rho l}{A}$$  
Here, $$l_{max}=2l,   A_{max}=2la$$ and $$l_{min}=l,  A_{min}=la$$
Thus, $$\displaystyle R_{max}=\frac{\rho l_{max}}{A_{min}}=\frac{\rho 2l}{la}=\frac{2\rho}{a}$$ and $$R_{min}=\dfrac{\rho l_{min}}{A_{max}}=\dfrac{\rho l}{2la}=\dfrac{\rho}{2a}$$
$$\implies \dfrac{R_{max}}{R_{min}}=4$$

Physics

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