The simple sum of two forces acting at a point is 16N and their s… - Vidyadip

MCQ

The simple sum of two forces acting at a point is $16N$ and their sum is $8N$ and its direction is perpendicular to the smaller force, then the forces are:

✓
$6N$ and $10N$
B
$8N$ and $8N$
C
$4N$ and $12N$
D
$2N$ and $14N$

✓

Answer

Correct option: A.

$6N$ and $10N$

Here $A + B = 16 ...(i)$
$\sqrt{\text{A}^2+\text{B}^2+2\text{AB}\cos\theta}=8\dots(\text{ii})$
and $\tan90^\circ=\frac{\text{B}\sin\theta}{\text{A}+\text{B}\cos\theta}$
or $\text{A}+\text{B}\cos\theta=\frac{\text{B}\sin\theta}{\tan90^\circ}=0$
or $\text{B}\cos\theta=-\text{A}$ or $\cos\theta=\frac{-\text{A}}{\text{B}}$
From $(ii), \text{A}^2+\text{B}^2+2\text{AB}\Big(\frac{-\text{A}}{\text{B}}\Big)=64$
or $B^2 - A^2 = 64$
Solving $(i)$ and $(iii),$ we get
$A = 6N$ and $B = 10N.$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Motion in a Plane→Motion in a Plane — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The graph between $\sqrt E $and $\frac{1}{p}$ is ($E$=kinetic energy and $p = $ momentum)

If we do an experiment by swinging a small ball by a thread of length $100\ cm,$ what will be the approximate time for complete to and froperiodic motion?

A stretched string of length $l,$ fixed at both ends can sustain stationary waves of wavelength $\lambda ,$ given by

A closed cubical box is completely filled with water and is accelerated horizontally towards right with an acceleration α. The resultant normal force by the water on the top of the box.

A rigid body is rotating with variable angular velocity $(a - bt)$ at any instant of time $ t.$ The total angle subtended by it before coming to rest will be ($a$ and $b$ are constants)

A particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $a_c$ is varying with time $t$ as, $a_c = k^2rt^2,$ the power delivered to the particle by the forces acting on it is

A mass of $20\, kg$ moving with a speed of $10\,m/s$ collides with another stationary mass of $5\,kg.$ As a result of the collision, the two masses stick together. The kinetic energy of the composite mass will be ............. $J$

A small object is placed at the center of a large evacuated hollow spherical container. Assume that the container is maintained at $0 K$. At time $t =0$, the temperature of the object is $200 K$. The temperature of the object becomes $100 K$ at $t = t _1$ and $50 K$ at $t = t _2$. Assume the object and the container to be ideal black bodies. The heat capacity of the object does not depend on temperature. The ratio $\left( t _2 / t _1\right)$ is. . . . .

The expansion in volume of a substance due to increase in temperature does not depend :

The displacement of a particle moving on a circular path of radius $r$ when it makes $60^\circ$ at the centre is: