Four forces are acting at a point P in equilibrium as shown in figure. The ratio of force $\mathrm{F}_{1}$ to $\mathrm{F}_{2}$ is $1: \mathrm{x}$ where $\mathrm{x}=$ ______.

JEE Main · 2022 · 25 Jul 2022 · Shift 1 · Laws of Motion

Four forces are acting at a point P in equilibrium as shown in figure. The ratio of force

F_{1}

F_{2}

1 : x

where

x =

______.

Answer: 3

Solution

For equilibrium, resolve forces along x and y directions. From the geometry (angle

θ = 4 5^{\circ}

), taking components:

F_{1} = 2 - \frac{1}{2} = \frac{2 - 1}{2} = \frac{1}{2}

and

F_{2} = 2 + \frac{1}{2} = \frac{2 + 1}{2} = \frac{3}{2}

. Therefore,

\frac{F _{1}}{F _{2}} = \frac{1/ 2}{3/ 2} = \frac{1}{3}

, giving

x = 3

JEE Main · 2022 · 25 Jul 2022 · Shift 1 · Integer answer

Practise more: all JEE Main PYQs on Laws of Motion →

More JEE Main questions on Laws of Motion

A simple pendulum has a bob with mass $m$ and charge q . The pendulum string has negligible mass. When a uniform and horizontal electric field $E$ is applied, the tension in the string changes. The final tension in the string, when pendulum attains an equilibrium positi …
JEE Main 2026View solution →
A large drum having radius R is spinning around its axis with angular velocity $ω$ , as shown in figure. The minimum value of $ω$ so that a body of mass M remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mas …
JEE Main 2026View solution →
A spring of force constant $15 N / m$ is cut into two pieces. If the ratio of their length is $1 : 3$ , then the force constant of smaller piece is ______ $N / m$
JEE Main 2026View solution →
In the given figure the blocks A, B and C weigh 4 kg, 6 kg and 8 kg respectively. The co-efficient of sliding friction between any two surfaces is 0.5. The force $F$ required to slide the block C with constant speed is ______ N. (Used …
JEE Main 2026View solution →
A block of mass 5 kg is moving on an inclined plane which makes an angle of $3 0^{\circ}$ with the horizontal. Friction coefficient between the block and inclined plane surface is $\frac{3}{2}$ . The force to be applied on the block so that the block will move down witho …
JEE Main 2026View solution →
A particle of mass m falls from rest through a resistive medium having resistive force, $F = - kv$ , where v is the velocity of the particle and k is a constant. Which of the following graphs represents velocity (v) versus time(t)?
JEE Main 2026View solution →