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Test: Lami's Theorem - Mechanical Engineering MCQ


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10 Questions MCQ Test - Test: Lami's Theorem

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Test: Lami's Theorem - Question 1


Force in the cable AB shown in the above figure is

Detailed Solution for Test: Lami's Theorem - Question 1

Concept:
Lami's Theorem:- It states that when three forces acting at a point are in equilibrium, then each force is proportional to the sine of the angle between the other two forces.

So according to the theorem.


Let,
Force in member AB = FAB
Force in member BC = FBC
from fig α = 90° + 30°  = 120°
β = 90° + 60° = 150°
γ = 90°
From Lami's theorem,

Hence the correct answer is an option (1) i.e 100√3 N.

Test: Lami's Theorem - Question 2


Above equation represents which of the following?

Detailed Solution for Test: Lami's Theorem - Question 2

Detailed Explanation:
Lami's Theorem states that, "If three coplanar forces acting at a point be in equillibrium, then each force is proportional to the sine of the angle betweenthe other two".
Let us consider three forces A, B, and C acting on a particle or a rigid body making angles α, β, and γ with each other, then

Additional Information
Lambert's Law:

  • It is related to Illumination.
  • Lambert's cosine law: It states that illumination, E at any point on a surface is directly proportional to the cosine of the angle between the normal at that point and the line of flux.
  • Law of Inverse Squares: The illumination of a surface is inversely proportional to the square of the distance between the surface and the light source

E = I/d2
Where E = Illuminance
I = Luminous Intensity
D = Distance between the surface and the source

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Test: Lami's Theorem - Question 3

A string whose extreme A is fixed has weights W1 and W2 attached to it at B and C, respectively, and passes around a smooth peg D carrying a weight of 730 N at the free end E. If in a state of equilibrium, BC is horizontal and AB and CD make angles of 135° and 110°, respectively, with BC, the weights W1 and W2 will be ______ and ______, respectively.

Detailed Solution for Test: Lami's Theorem - Question 3

Lami's theorem:
It states that if three forces acting at a point are in equilibrium, each force is proportional to the sine of the angle between the other two forces.
Consider three forces FA, FB, and FC acting on a particle or rigid body making angles α, β, and γ with each other.

Then from Lami's theorem,

Calculation:
Given:
W = 730 N, And the pulley is smooth.
First string ABCD is split into two parts and consider the joints B and C separately.
Let, T1 = Tension in String AB, T2 = Tension in String BC, T3 = Tension in String CD, T4 = Tension in String DE

Since at joint B and C, three forces are acting on both points. But at B all three forces are unknown and at point C only two forces are unknown. So Apply Lami's theorem first at joint C:
∵ Pulley is smooth, T3 = T4 = 730 N
 Apply Lami's theorem first at joint C:

⇒ T2 = 249.674 N And W2 = 685.98 N
Now, the value of T2 is known at point B.
Apply Lami's theorem first at joint B:

Test: Lami's Theorem - Question 4

A body acted upon by three coplanar forces P1, P2 and P3 (as shown in figure) is in equilibrium. Which of the following is correct? [where, "O" is the point of concurrency of the forces]

Detailed Solution for Test: Lami's Theorem - Question 4

LAMI’S THEOREM:

  • If a system of Three forces is in equilibrium, then, each force of the system is proportional to sine of the angle between the other two forces (and constant of proportionality is the same for all the forces). Thus, we have,


The formula for Lami's Theorem:

Calculation:
Given:

A = P1, B = P2 = 300N, C = P3, and
α = 90° + 30° = 120°, β = 90° + 60° = 150° and  γ = 360° - 120° - 150° = 90°
on salving 

P3 = 600N
only option 1 is correct.

Test: Lami's Theorem - Question 5

If point A is in equilibrium under the action of the applied forces, the values of tension. TAC = ?

Detailed Solution for Test: Lami's Theorem - Question 5

Lami's theorem:
It states that if three forces acting at a point are in equilibrium, each force is proportional to the sine of the angle between the other two forces. Consider three forces FA, FB, FC acting on a particle or rigid body making angles α, β and γ with each other.

Therefore, 
Calculation:
Given:

We have angle BAC = 180° - (30° + 60°)
angle BAC = 90°
By Lami’s Theorem, 
TAC = 400 N

Test: Lami's Theorem - Question 6

According to Lami’s theorem, if three coplanar forces are acting at a point b in equilibrium, then each force is proportional to the ______ of the angle between the other two.

Detailed Solution for Test: Lami's Theorem - Question 6

Lami's theorem:
It states that if three forces acting at a point are in equilibrium, each force is proportional to the sine of the angle between the other two forces.
Consider three forces FA, FB, FC acting on a particle or rigid body making angles α, β and γ with each other.

Then from Lami's theorem,

Test: Lami's Theorem - Question 7

Three coplanar forces A, B and C acting at a point in the plane are in equilibrium. If the given value of A is 1.9318 kg wt and sinθ1 is 0.9659, what is the value of C?

Test: Lami's Theorem - Question 8

If three forces, acting at a point, be in equilibrium then each force is proportional to the sine of the angle between the other two. This theorem is called

Detailed Solution for Test: Lami's Theorem - Question 8

Lami's theorem:
It states that if three forces acting at a point are in equilibrium, each force is proportional to the sine of the angle between the other two forces.
Consider three forces FA, FB, FC acting on a particle or rigid body making angles α, β and γ with each other.

Therefore,

Important Points
Triangle Law of Forces: It states that if two forces acting simultaneously on a particle, be represented in magnitude and direction by the two sides of a triangle, taken in order; their results may be represented in magnitude and direction by the third side of the triangle, taken in the opposite order.”

Law of the parallelogram of force: 
It states that if two forces, acting at the point of a body, be represented in magnitude and direction by the two adjacent sides of a parallelogram, then their resultant is represented in magnitude and direction by the diagonal of the parallelogram contained in between the two adjacent forces.

Test: Lami's Theorem - Question 9

What is the minimum number of non-zero vectors in different planes that can be added to give a resultant of zero?

Test: Lami's Theorem - Question 10

If the body is under equilibrium under the influence of a set of non-colinear force, then the minimum number of forces has to be

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