Physics - Motion of System of Particles and Rigid Body

Question - 1

In the HCI molecule, the separation between the nuclei of the two atoms is about 1.27 A (1A  =  \({ 10 }^{ -10 }\)  m). Givan that, chlorine atom is about 35.5 times as massive as a hydrogen atom and all the mass of the atom is concentrated in its nuclueus. the approximate location of center of mass w.r.t H atom is

  • A 1\(\overset { \circ }{ A } \)
  • B 1.24 \(\overset { \circ }{ A } \)
  • C ?\({ 10 }^{ -10 }\)?  \(\overset { \circ }{ A } \)
  • D \({ 10 }^{ -5 }\)\(\overset { \circ }{ A } \)

Question - 2

Two spherical bodies of mass M and 5 M and radii R and 2 R respectively are released in free space with initial separation between their centre equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is

  • A 1.5 R
  • B 2.5 R
  • C 4.5 R
  • D 7.5 R

Question - 3

If linear density of a rod of length 3m varies as  \(\lambda \)  = 2 + X, then the position of the centre of gravity of the rod is

  • A \(\frac { 7 }{ 3 } m\)
  • B \(\frac { 12 }{ 7 } m\)
  • C \(\frac { 10 }{ 7 } m\)
  • D \(\frac { 9 }{ 7 } m\)

Question - 4

Four particle of masses, m, 2 m, 3 m and 4 m are arranged at the corners of a parallogram with each side equal to a and one of the angle between two adjacent sides is   \({ 60 }°\) . The parallelogram lies in the xy plane with mass m at the origin and 4 m on the X-axis, The centre of mass of the arrangement will be located at

  • A \((\frac { \sqrt { 3 } }{ 2 } a,0.95a)\)
  • B \((0.95a,\frac { \sqrt { 3 } }{ 4 } a)\)
  • C \((\frac { 3a }{ 4 } ,\frac { a }{ 2 } )\)
  • D \(( \frac { a }{ 2 } ,\)\(\frac { 3a }{ 4 } )\)

Question - 5

A particle of mass 2 Kg moving with a velocity 5i m/s collides head on with another particle of mass 3Kg moving with a velocity - 2i m/s. After the collision, the first particle has speed of 1.6i m/s in negative x-direction. Then, velocity of second particle after collision is

  • A 0 m/s
  • B  2.4i m/s
  • C 5i m/s
  • D 10i m/s

Question - 6

Two persons each of mass m are standing at the two extremes of a rail road car of mass M resting on a smooth track. The person on the left jumps with a horizontal velocity u with respect to the state of the car before the jump. thereafter, the other person jumps to the car before jump. the velocity of the car after both have jumped down is

  • A Zero
  • B \(\frac { 2mu }{ (m+n) } \)
  • C \(\frac { { m }^{ 2 }u }{ M(M=m) } \)
  • D None of these

Question - 7

A point P on the rim of wheel is initially at rest and in contact with the ground. Find the displacement of the point P, if the radius of the wheel is 5 m and the wheel rolls forword through half a revolution.

  • A 5 m
  • B 10 m
  • C 2.5 m
  • D 5\(\sqrt { { (\pi }^{ 2 }+4) } m\)

Question - 8

The instanneous angular position of a point on a roting wheel is given by the equation \(\theta (t)=2{ t }^{ 3 }-6{ t }^{ 2 }\).The torque on the wheel becomes zero at

  • A t = 0.5 s
  • B t = 0.25 s
  • C t = 2 s
  • D t = 1 s

Question - 9

The moment of inertia of a thin uniform circular disc about one of its diameter is /. The moment of inertia about an axis perpendicular to the circuler surface and passing through its centre is

  • A 2l
  • B l /\(\sqrt { 2 } \)
  • C ?\(\sqrt { 2 } \)? l
  • D l / ?\(\sqrt { 2 } \)?

Question - 10

The moment of inertia of a uniform circuler disc of radius R and mass M about axis passing from the edge of the disc and normal to the disc is

  • A \(\frac { 1 }{ 2 } { MR }^{ 2 }\)
  • B \({ MR }^{ 2 }\)
  • C \(\frac { 7 }{ 2 } { MR }^{ 2 }\)
  • D \(\frac { 3 }{ 2 } { MR }^{ 2 }\)
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