☆quality answer needed☆》A physical quantity Q is given by the pe

1.	☆quality answer needed☆》A physical quantity Q is given by 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» 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. $\footnotesize\implies\sf \dfrac{\Delta Q}{Q} \times 100 =2 \bigg \{\dfrac{\Delta A}{A} \times 100 \bigg \} + \dfrac{3}{2} \bigg \{\dfrac{\Delta B}{B} \times 100 \bigg \} + 4\bigg \{\dfrac{\Delta C}{C} \times 100 \bigg \} + \dfrac{1}{2}\bigg \{\dfrac{\Delta D }{D} \times 100 \bigg \} \\\\$ $\footnotesize\bullet\:\tt\dfrac{\Delta A}{A} \times 100 = 1\%\\\\$ $\footnotesize\bullet\:\tt\dfrac{\Delta B}{B} \times 100 = 2\%\\\\$ $\footnotesize\bullet\:\tt\dfrac{\Delta C}{C} \times 100 = 4\%\\\\$ $\footnotesize\bullet\:\tt\dfrac{\Delta D}{D} \times 100 = 2\%\\\\$ $\footnotesize\implies\sf \dfrac{\Delta Q}{Q} \times 100 =2 \bigg \{ 1\%\bigg \} + \dfrac{3}{2} \bigg \{2 \%\bigg \} + 4\bigg \{4\%\bigg \} + \dfrac{1}{2}\bigg \{2\% \bigg \} \\\\$ $\footnotesize\implies\sf \dfrac{\Delta Q}{Q} \times 100 =2\% + 3 \% + 16\% + 1\% \\\\$ $\footnotesize\implies \gray{\underline{ \boxed{ \orange{\bf \dfrac{\Delta Q}{Q} \times 100 =22\%}}}} \\$

☆quality answer needed☆》A physical quantity Q is given by 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»

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.

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

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

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

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

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

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

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

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