Equilibrium of Concurrent Forces

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Three forces start acting simultaneously on a particle moving with velocity $v$ . These forces are represented in magnitude and direction by the three sides of a $Δ A B C$ (as shown). The particle will now move with velocity

v

(B)

greater than

v

(C)

∣ v ∣

in the direction of largest force

B C

(D)

v

, remaining unchanged

JEE Main 2020, 7 Jan Shift-II

LEVELJEE Main

A mass of 10 kg is suspended by a rope of length 4 m, from the ceiling. A force $F$ is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of $4 5^{\circ}$ with the vertical. Then, $F$ equals (Take, $g = 10 ms^{- 2}$ and the rope to be massless)

JEE Main 2021, 31 Aug Shift-II

LEVELJEE Main

Statement I If three forces $F_{1}, F_{2}$ and $F_{3}$ are represented by three sides of a triangle and $F_{1} + F_{2} = - F_{3}$ , then these three forces are concurrent forces and satisfy the condition for equilibrium. Statement II A triangle made up of three forces $F_{1}, F_{2}$ and $F_{3}$ as its sides taken in the same order, satisfy the condition for translatory equilibrium. In the light of the above statements, choose the most appropriate answer from the options given below.

(A)

Statement I is false but statement II is true.

(B)

Statement I is true but statement II is false.

(C)

Both statement I and statement II are false.

(D)

Both statement I and statement II are true.

JEE Main 2019, 9 Jan Shift-II

LEVELJEE Main

A mass of $10 kg$ is suspended vertically by a rope from the roof. When a horizontal force is applied on the mass, the rope deviated at an angle of $4 5^{\circ}$ at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is (Take, $g = 10 ms^{- 2}$ )

A light spring balance hangs from the hook of the other light spring balance and a block of mass $M$ kg hangs from the former one. Then, the true statement about the scale reading is

(A)

Both the scales read

M

kg each

(B)

The scale of the lower one reads

M

kg and of the upper one zero

(C)

The reading of the two scales can be anything but the sum of the readings will be

M

(D)

Both the scales read

M /2

JEE Main 2021, 1 Sep Shift-II

LEVELJEE Main

An object of mass $m$ is being moved with a constant velocity under the action of an applied force of $2 N$ along a frictionless surface with following surface profile. The correct applied force versus distance graph will be

Column II shows five systems in which two objects are labelled as $X$ and $Y$ . Also in each case a point $P$ is shown. Column I gives some statements about $X$ and/or $Y$ . Match these statements to the appropriate system(s) from Column II

List-I

(P)

The force exerted by

X

Y

has a magnitude

M g

(Q)

The gravitational potential energy of

X

is continuously increasing.

(R)

Mechanical energy of the system

X + Y

is continuously decreasing.

(S)

The torque of the weight of

Y

about point

P

is zero.

List-II

(1)

Block

Y

of mass

M

left on a fixed inclined plane

X

, slides on it with a constant velocity.

(2)

Two ring magnets

Y

and

Z

, each of mass

M

, are kept in frictionless vertical plastic stand so that they repel each other.

Y

rests on the base

X

and

Z

hangs in air in equilibrium.

P

is the topmost point of the stand on the common axis of the two rings. The whole system is in a lift that is going up with a constant velocity.

(3)

A pulley

Y

of mass

m_{0}

is fixed to a table through a clamp

X

. A block of mass

M

hangs from a string that goes over the pulley and is fixed at point

P

of the table. The whole system is kept in a lift that is going down with a constant velocity.

(4)

A sphere

Y

of mass

M

is put in a non-viscous liquid

X

kept in a container at rest. The sphere is released and it moves down in the liquid.

(5)

A sphere

Y

of mass

M

is falling with its terminal velocity in a viscous liquid

X

kept in a container.

JEE Advanced 1978

LEVELJEE Advanced

A rigid insulated wire frame in the form of a right angled triangle $A B C$ , is set in a vertical plane as shown in figure. Two beads of equal masses $m$ each and carrying charges $q_{1}$ and $q_{2}$ are connected by a cord of length $l$ and can slide without friction on the wires. Considering the case when the beads are stationary determine (a) (i) The angle $α$ (ii) The tension in the cord (iii) The normal reaction on the beads (b) If the cord is now cut what are the value of the charges for which the beads continue to remain stationary?

LEVELJEE Main

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle $θ$ should be (2001)

(A)

0^{\circ}

(B)

3 0^{\circ}

(C)

4 5^{\circ}

(D)

6 0^{\circ}

LEVELJEE Main

A string of negligible mass going over a clamped pulley of mass $m$ supports a block of mass $M$ as shown in the figure. The force on the pulley by the clamp is given by (2001)

(A)

2 M g

(B)

2 m g

(C)

g (M + m)^{2} + m^{2}

(D)

g (M + m)^{2} + M^{2}

JEE Main 2021

LEVELJEE Advanced

One end of a horizontal uniform beam of weight W and length L is hinged on a vertical wall at point O and its other end is supported by a light inextensible rope. The other end of the rope is fixed at point Q, at a height L above the hinge at point O. A block of weight $α W$ is attached at the point P of the beam, as shown in the figure (not to scale). The rope can sustain a maximum tension of $(22) W$ . Which of the following statement(s) is(are) correct ?

* Multiple Correct Options

(A)

The vertical component of reaction force at O does not depend on

α

(B)

The horizontal component of reaction force at O is equal to W for

α = 0.5

(C)

The tension in the rope is 2W for

α = 0.5

(D)

The rope breaks if

α > 1.5

List-I

List-II

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle θ should be (2001)

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A string of negligible mass going over a clamped pulley of mass m supports a block of mass M as shown in the figure. The force on the pulley by the clamp is given by (2001)

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle $θ$ should be (2001)

A string of negligible mass going over a clamped pulley of mass $m$ supports a block of mass $M$ as shown in the figure. The force on the pulley by the clamp is given by (2001)