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Laws of Motion · Question 56

AIPMT 2006MCQMedium📈 Topic in 38% papers+4−1
1

A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity . The force exerted by the liquid at the other end is

  1. ML2 22
  2. ML 22
  3. ML2 2
  4. ML 2

Answer

(2) ML 22

Solution

Mass per unit length of the liquid = ML.

Consider an element of length dx at a distance x from the axis: dm = MLdx

centripetal force needed by it, dF = (dm) 2 x = ML 2 x dx

This force is finally supplied by the closed far end of the tube, so the liquid presses on that end with

F = 0L ML 2 x dx

= M 2L L22

= ML 22

(Equivalently, the whole mass M moves as if concentrated at its centre of mass at L2.)

Answer: (2)

AIPMT 2006

Keep practising — Laws of Motion

2

A bomb of mass 30 kg at rest explodes into two pieces of masses 18 kg and 12 kg. The velocity of 18 kg mass is 6 m s-1. The kinetic energy of the other mass is :

  1. 324 J
  2. 486 J
  3. 256 J
  4. 524 J
AIPMT 2005
3

A block of mass m is placed on a smooth wedge of inclination . The whole system is accelerated horizontally so that the block does not slip on the wedge. The force exerted by the wedge on the block will be (g is acceleration due to gravity)

  1. mg
  2. mg
  3. mg
  4. mg/
AIPMT 2004
4

The coefficient of static friction, s, between block A of mass 2 kg and the table as shown in the figure is 0.2. What would be the maximum mass value of block B so that the two blocks do not move? The string and the pulley are assumed to be smooth and massless. (g = 10 m/s2) [figure]

  1. 2.0 kg
  2. 4.0 kg
  3. 0.2 kg
  4. 0.4 kg
AIPMT 2004
5

A man weighs 80 kg. He stands on a weighing scale in a lift which is moving upwards with a uniform acceleration of 5 m/s2. What would be the reading on the scale ? (g = 10 m/s2)

  1. zero
  2. 400 N
  3. 800 N
  4. 1200 N
AIPMT 2003
6

A monkey of mass 20 kg is holding a vertical rope. The rope will not break when a mass of 25 kg is suspended from it but will break if the mass exceeds 25 kg. What is the maximum acceleration with which the monkey can climb up along the rope ? (g = 10 m/s2)

  1. 5 m/s2
  2. 10 m/s2
  3. 25 m/s2
  4. 2.5 m/s2
AIPMT 2003
7

A stationary particle explodes into two particles of masses m1 and m2 which move in opposite directions with velocities v1 and v2. The ratio of their kinetic energies E1/E2 is :

  1. m2/m1
  2. m1/m2
  3. 1
  4. m1v2/m2v1
AIPMT 2003
8

An object of mass 3 kg is at rest. Now a force of F = 6t2 i + 4t j is applied on the object then velocity of object at t = 3 sec. is

  1. 18 i + 3 j
  2. 18 i + 6 j
  3. 3 i + 18 j
  4. 18 i + 4 j
AIPMT 2002
9

A lift of mass 1000 kg which is moving with acceleration of 1 m/s2 in upward direction, then the tension developed in string which is connected to lift is

  1. 9800 N
  2. 10,800 N
  3. 11,000 N
  4. 10,000 N
AIPMT 2002
10

A block of mass 10 kg placed on rough horizontal surface having coefficient of friction = 0.5, if a horizontal force of 100 N acting on it then acceleration of the block will be

  1. 10 m/s2
  2. 5 m/s2
  3. 15 m/s2
  4. 0.5 m/s2
AIPMT 2002
11

On the horizontal surface of a truck a block of mass 1 kg is placed ( = 0.6) and the truck is moving with acceleration 5 m/s2, then the frictional force on the block will be

  1. 5 N
  2. 6 N
  3. 5.88 N
  4. 8 N
AIPMT 2001

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