Question

The coefficients of linear expansion of P and Q are ${\alpha }_1$ and ${\alpha }_2$ respectively. If the coefficient of cubical expansion of Q is three times the coefficient of superficial expansion of P, then which of the following is true ?

• A. ${\alpha }_2=2{\alpha }_1$
• B. ${\alpha }_1=2{\alpha }_2$
• C. ${\alpha }_2=3{\alpha }_1$
• D. ${\alpha }_1=3{\alpha }_2$

Answer 1

Answer: (A)

${\alpha }_2=2{\alpha }_1$

First we note that coefficient of cubical expansion = 3 x coefficient of linear expansion
Coefficient of superficial expansion = 2 x coefficient of linear expansion
Now it is given that coefficient of cubical expansion of Q is three times the coefficient of superficial expansion of P.
So, 3 x coefficient of linear expansion of Q = 3 x 2 x coefficient of linear expansion of P
So ${\alpha }_2$ = 2 x ${\alpha }_1$