Question

A dimensionless quantity Y is represented by the formula
$y = \frac{a - bc}{d + e}$
Which of the Following is/are correct?
A) Dimensions of d and e are same
B) abc and de have same dimensions
$c) \: \frac{bc}{ae + d} \: is \: dimentionless$
D) de + bc is not meaningful
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Answer 1

answer : (a), (b) , (d)

explanation : given expression, y = (a - bc)/(d + e)

a/c to question, y is dimensionless quantity.

it means dimension of (a - bc) = dimension of (d + e) .....(i)

also dimension of a = dimension of bc....(ii)

dimension of d = dimension of e....(iii)

now Let's check options,

(a) dimension of d and e are same .of course it is true. [ from equation (iii)]

hence, option (a) is correct

(b) abc and de have same dimensions.

from equations (i), (ii) and (iii),

dimension of a = dimension of d

and dimension of bc = dimension of e

multiplying both equations,

dimension of abc = dimension of de

hence, it is correct.so, option (b) is also correct.

(c) bc/(ae + d) is dimensionless. this is not true statement because dimension of d = dimension of e not ae.

so, option (c) is incorrect.

(d) (de + bc) is not meaningful. yeah, it is correct that (de + bc) is not meaningful statement because dimension of de ≠ dimension of bc