The coefficients of linear expansion of P and Q are α1 and α2 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?

Question

The coefficients of linear expansion of P and Q are α1 and α2 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) α2 = 2α1 (B) α1 = 2α2 (C) α2 = 3α1 (D) α1 = 3α2

Tardigrade Admin · Accepted Answer

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 \times

coefficient of linear expansion of

Q = 3 \times 2 \times

coefficient of linear expansion of

P

So

α_{2} = 2 \times α_{1}

Q. The coefficients of linear expansion of P and Q are $α_{1}$ and $α_{2}$ 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?

$α_{2} = 2 α_{1}$

$α_{1} = 2 α_{2}$

$α_{2} = 3 α_{1}$

$α_{1} = 3 α_{2}$

Q. The coefficients of linear expansion of P and Q are α1​ and α2​ 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?

α2​=2α1​

α1​=2α2​

α2​=3α1​

α1​=3α2​

Q. The coefficients of linear expansion of P and Q are $α_{1}$ and $α_{2}$ 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?

$α_{2} = 2 α_{1}$

$α_{1} = 2 α_{2}$

$α_{2} = 3 α_{1}$

$α_{1} = 3 α_{2}$