Dynamics & Statics [IAS (Admin.) Mains Mathematics]: Questions 1 - 6 of 60

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Question 1

Appeared in Year: 2016

Describe in Detail Subjective▾

Two weight and are suspended from fixed point by strings and are kept apart by a light rod If the strings and make angles and with rod , show that the angle which the rod makes with the vertical is given by

[CS (Main) Paper 1]

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Explanation

The rod kept apart the strings and carring weights and respectively, at its ends.

The Rod AB Kept Apart the Strings OA and OB

The thrust of the rod at will be equal and opposite to that at in shown in Figure.

Let b…

… (635 more equations, 27 figures) …

Question 2

Appeared in Year: 2015

Describe in Detail Subjective▾

Write down precisely the conservation theorems for energy, linear momentum and angular momentum of a particle with their mathematical forms. (15 Marks)

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Explanation

  • Conservation of linear momentum:- It follows from Newton՚s second law of motion in the from
  • That is, if the total force F is zero then and the linear…

… (179 more equations) …

Question 3

Appeared in Year: 2002

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Two spaceships are moving at a velocity of relative to the earth in opposite directions. What is the speed of one spaceship relation to the other? (20 Marks)

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Explanation

… (81 more equations, 6 figures) …

Question 4

Appeared in Year: 2013

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A particle describes a circular motion under influence of an attractive central force directed toward a point on the circle. Show that force varies as the inverse fifth power of distance.

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Explanation

In rectangular coordinates, the equation of the circle is with center

We could plug in

… (359 more equations) …

Question 5

Appeared in Year: 2016

Describe in Detail Subjective▾

Find the centre of mass of a homogeneous semicircular plate of radius .

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Explanation

  • Here too the centre of mass obviously lies on the line of symmetry (Fig (1) ) passing through the mid – point of the base and perpendicular to it. Since it is a homogeneous plate, the centre of the mass will be at a distance from , given by relation

… (283 more equations, 9 figures) …

Question 6

Appeared in Year: 2016

Describe in Detail Subjective▾

Calculate the percentage contraction in the length of the rod in a frame of reference moving with velocity in a direction (1) parallel to its length and (2) at an angle of with its length. What is the orientation of the rod in the moving frame of reference in case.

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Explanation

(1)

Let be the length of the rod, placed along the axis of , in a reference frame , at rest. Then, its length in a frame moving with velocity , relative to in a direction parallel to its length i.e.. along the axis of is given by

… (595 more equations) …