The sum of the magnitudes of two forces acting at a point is $18 N$ and the magnitude of their resultant is $12 N$ . If the resultant makes an angle of $90^{o}$ with the force of smaller magnitude, what are the magnitudes of the two forces?

Open in App

Solution

It is a right angled triangle with larger magnitude force forming hypotenuse as the resultant makes an angle of $90^{\circ}$

Hence $B^{2} = R^{2} + A^{2}$

$R^{2} = B^{2} - A^{2}$

$A + B = 18$

On substituting the value

$B = 18 - A$

On substituting the value of $B$ in equation above and solving we get

$A = 5 a n d B = 13$

Suggest Corrections

Similar questions

Q. The sum of the magnitudes of two forces is

18 N

and the magnitude of their resultant is

12 N

. If the resultant makes an angle of

90^{\circ}

with the smaller force, then find the magnitude of the forces.

Q. Two force are such that the sum of their magnitudes is

18 N

and their resultant is perpandicular to the smaller force and magnitude of resultant is

12 N

. Then the magnitudes of the force are

Q. The sum of magnitudes of two forces acting at a point is

16 N

and their resultant

8 \sqrt{3} N

is at

90^{o}

with the force of smaller magnitude. The two forces (in

N

) are

Q. Two forces are such that the sum of their magnitudes is

18 N

and their resultant is perpendicular to the smaller force and magnitude of resultant is

12 N

. Then the magnitude of the forces are

Two forces are such that the sum of their magnitudes is 18 N and their resultant is perpendicular to the smaller force and magnitude of resultant is 12 N. Then the magnitudes of the forces are

Join BYJU'S Learning Program

The sum of the magnitudes of two forces acting at a point is 18N and the magnitude of their resultant is 12N . If the resultant makes an angle of 90o with the force of smaller magnitude, what are the magnitudes of the two forces?

It is a right angled triangle with larger magnitude force forming hypotenuse as the resultant makes an angle of90∘ Hence B2=R2+A2 R2=B2−A2 A+B=18 On substituting the value B=18−A On substituting the value of B in equation above and solving we get A=5andB=13

The sum of the magnitudes of two forces acting at a point is $18 N$ and the magnitude of their resultant is $12 N$ . If the resultant makes an angle of $90^{o}$ with the force of smaller magnitude, what are the magnitudes of the two forces?