Question

Two forces p and Q acting at a point maximum resultant is 300 N and minimum magnitude is 800 N find the value of p and Q​

​

Answer 1

Explanation:

Two force P and Q .

Maximum resultant = 300.

Minimum resultant = 800 N.

TO FIND :-

The value of P and Q.

SOLUTION :-

The maximum resultant force can be written as,

\begin{gathered} \implies \sf \: P + Q = 300....(1) \\ \end{gathered}

⟹P+Q=300....(1)

The minimum resultant force can be written as,

\begin{gathered}\implies \sf \: P - Q = 800....(2) \\ \end{gathered}

⟹P−Q=800....(2)

From equation 1 we have,

\begin{gathered}\implies \sf \: P = 300 - Q ....(3) \\ \end{gathered}

⟹P=300−Q....(3)

From equation 2 we have,

\begin{gathered}\implies \sf \: P = 800 + Q ....(4) \\ \end{gathered}

⟹P=800+Q....(4)

On comparing equation 3 and 4 we get,

\begin{gathered}\implies \sf \: 300 - Q = 800 + Q \\ \end{gathered}

⟹300−Q=800+Q

\begin{gathered}\implies \sf \: - 2Q = 500 \\ \end{gathered}

⟹−2Q=500

\begin{gathered}\implies \sf \: - Q = \dfrac{500}{2} \\ \end{gathered}

⟹−Q=

2

500

\begin{gathered}\implies \sf \: Q = - 250 \\ \end{gathered}

⟹Q=−250

Now substitute the value of Q in equation 1,

\begin{gathered}\implies \sf \: P - 250 = 300 \\ \end{gathered}

⟹P−250=300

\begin{gathered}\implies \sf \: P= 300 + 250 \\ \end{gathered}

⟹P=300+250

\implies \sf \: P=550⟹P=550

Hence the value of P is 550 and value of Q is -250.

Thank you ☺️

Answer 2

Answer:

• $\textsf{Value of P is 550}$
• $\textsf{Value of Q is -250}$

Explanation:

$\star\:{\underline{\underline{\tt{\red{GIVEN}}}}}:-$

• $\sf{Two \:force\: P\: and\: Q }$
• $\sf{Resultant_{\:(Max)} = 300N}$
• $\sf{Resultant_{\:(Min)} = 800 N}$

$\star\:{\underline{\underline{\tt{\orange{TO\: FIND }}}}}:-$

• $\sf{The \:value \:of\: P \:and \:Q}$

$\star\:{\underline{\underline{\tt{\green{SOLUTION}}}}}:-$

• $\textsf{P + Q = 300 N . . . . ( 1 )}$
• $\textsf{P = 300 - Q . . . . ( 2 )}$
• $\textsf{P - Q = 800 N . . . . ( 3 )}$
• $\textsf{P = 800 + Q . . . . ( 4 )}$

$\dag\:\underline{\mathfrak{\purple{By\: comparing \: equation\:(2) \:and\:(3)}}}:-$

$\qquad\quad\rightarrow\:\:\:\:\sf\orange{ 300 - Q = 800 + Q}$

$\qquad\quad\rightarrow\:\:\:\:\sf\blue{ - 2Q = 500}$

$\qquad\quad\rightarrow\:\:\:\:\sf\orange{ - Q = \dfrac{500}{2} }$

$\qquad\quad\rightarrow\:\:\:\:\sf\blue{ Q = - 250}$

$\dag\:\underline{\mathfrak{\purple{Substituting \:the \:value \:of\: Q \:in\: equation\: (1)}}}:-$

$\qquad\quad\rightarrow\:\:\:\:\sf\orange{ P - 250 = 300 }$

$\qquad\quad\rightarrow\:\:\:\:\sf\blue{ P= 300 + 250 }$

$\qquad\quad\rightarrow\:\:\:\:\sf\orange{ P=550}$

$\dag\:\underline{\mathfrak{\purple{Hence,}}}:-$

• $\sf\red{Value \ of \ P \ is \ 550}$
• $\sf\green{Value \ of \ Q \ is \ -250}$