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JEE Main

Exam: JEE Main
Subject: Physics
Chapter: Mathematics in Physics

JEE Main · Physics · Mathematics in Physics

Sum of magnitude of two forces is 25 ~N . The resultant of these...

Sum of magnitude of two forces is

25 \mathrm{~N}

. The resultant of these forces is normal to the smaller force and has a magnitude of

10 \mathrm{~N}

. Then the two forces are

Options

A $14.5 \mathrm{~N}, 10.5 \mathrm{~N}$
B $16 \mathrm{~N}, 9 \mathrm{~N}$
C $13 \mathrm{~N}, 12 \mathrm{~N}$
D $20 \mathrm{~N}, 5 \mathrm{~N}$

Correct answer

A. $14.5 \mathrm{~N}, 10.5 \mathrm{~N}$

Step-by-step solution

Sum of two forces

F_1+F_2=25

Resultant of these forces

(10)^2=F_1^2+F_2^2+2 F_1 F_2 \cos \theta

Since, resultant is normal to the smaller force

\therefore \quad F_1+F_2 \cos \theta=0

From Eqs. (i), (ii) and (iii), we get

\begin{gathered} F_1=14.5 \mathrm{~N} \\ F_2=10.5 \mathrm{~N} \end{gathered}

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