Question

☆quality answer needed☆
》A physical quantity Q is given by
$q = \frac{ {a}^{2} {b}^{ \frac{3}{2} } }{ {c}^{4} {d}^{ \frac{1}{2} } }$
the percentage errors in the A,B,C,D are 1%,2%,4%,2% respectively. find the percentage error in Q.


it is class 11th question
DON'T SPAM. ​

Answer 1

Answer:

A physical quantity Q is given by :

$\footnotesize\implies\sf Q = \dfrac{ {A}^{2} {B}^{ \frac{3}{2} } }{ {C}^{4} {D}^{ \frac{1}{2} } }$

• The percentage errors in the A,B,C,D are 1%,2%,4%,2% respectively.

$\footnotesize\implies\sf \dfrac{\Delta Q}{Q} \times 100 =2 \bigg \{\dfrac{\Delta A}{A} \times 100 \bigg \} + \dfrac{3}{2} \bigg \{\dfrac{\Delta B}{B} \times 100 \bigg \} + 4\bigg \{\dfrac{\Delta C}{C} \times 100 \bigg \} + \dfrac{1}{2}\bigg \{\dfrac{\Delta D }{D} \times 100 \bigg \}$

$\footnotesize\bullet\:\tt\dfrac{\Delta A}{A} \times 100 = 1\%$

$\footnotesize\bullet\:\tt\dfrac{\Delta B}{B} \times 100 = 2\%$

$\footnotesize\bullet\:\tt\dfrac{\Delta C}{C} \times 100 = 4\%$

$\footnotesize\bullet\:\tt\dfrac{\Delta D}{D} \times 100 = 2\%$

$\footnotesize\implies\sf \dfrac{\Delta Q}{Q} \times 100 =2 \bigg \{ 1\%\bigg \} + \dfrac{3}{2} \bigg \{2 \%\bigg \} + 4\bigg \{4\%\bigg \} + \dfrac{1}{2}\bigg \{2\% \bigg \}$

$\footnotesize\implies\sf \dfrac{\Delta Q}{Q} \times 100 =2\% + 3 \% + 16\% + 1\%$

$\footnotesize\implies \gray{\underline{ \boxed{ \orange{\bf \dfrac{\Delta Q}{Q} \times 100 =22\%}}}}$

Answer 2

Answer:

$\underline{\purple{\ddot{\Mathsdude}}}$

♧Answered by Rohith kumar maths dude :-

I posted your answer on attachment refer it .

I tried it well to answer.

♧♧Thank you.

♧♧Hope it helps u mate .