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Motion in a Plane · Question 40

AIPMT 2005MCQMedium📈 Topic in 0% papers+4−1
1

Two boys are standing at the ends A and B of a ground where AB = a. The boy at B starts running in a direction perpendicular to AB with velocity v1. The boy at A starts running simultaneously with velocity v and catches the other in a time t, where t is

  1. a v2 + v12
  2. av + v1
  3. av - v1
  4. a2v2 - v12

Answer

(4) a2v2 - v12

Solution

In time t, boy B moves v1 t perpendicular to AB, while boy A runs straight to the meeting point, covering vt.

AB, B's path and A's path form a right-angled triangle with A's path as hypotenuse:

(vt)2 = a2 + (v1 t)2

t2(v2 - v12) = a2

t = a2v2 - v12

Answer: (4)

AIPMT 2005

Keep practising — Motion in a Plane

2

A stone tied to the end of a string of 1 m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolutions in 44 seconds, what is the magnitude and direction of acceleration of the stone?

  1. 2 m s-2 and direction along the radius towards the centre
  2. 2 m s-2 and direction along the radius away from the centre
  3. 2 m s-2 and direction along the tangent to the circle
  4. 2/4 m s-2 and direction along the radius towards the centre.
AIPMT 2005
3

If the angle between the vectors A and B is , the value of the product ( B A ) A is equal to

  1. BA2
  2. BA2
  3. BA2
  4. zero.
AIPMT 2005
4

If a vector 2 i + 3 j + 8 k is perpendicular to the vector 4 j - 4 i + k, then the value of is

  1. 1/2
  2. -1/2
  3. 1
  4. -1.
AIPMT 2005
5

If | A B| = 3 A B then the value of | A + B| is

  1. (A2 + B2 + AB)1/2
  2. (A2 + B2 + AB 3 )1/2
  3. A + B
  4. (A2 + B2 + 3AB)1/2
AIPMT 2004
6

The vector sum of two forces is perpendicular to their vector differences. In that case, the forces

  1. are equal to each other
  2. are equal to each other in magnitude
  3. are not equal to each other in magnitude
  4. cannot be predicted.
AIPMT 2003
7

A particle moves along a circle of radius ( 20 ) m with constant tangential acceleration. If the velocity of the particle is 80 m/s at the end of the second revolution after motion has begun, the tangential acceleration is

  1. 40 m/s2
  2. 640 m/s2
  3. 160 m/s2
  4. 40 m/s2
AIPMT 2003
8

A particle A is dropped from a height and another particle B is projected in horizontal direction with speed of 5 m/sec from the same height then correct statement is

  1. particle A will reach at ground first with respect to particle B
  2. particle B will reach at ground first with respect to particle A
  3. both particles will reach at ground simultaneously
  4. both particles will reach at ground with same speed.
AIPMT 2002
9

If | A + B | = | A | + | B |, then angle between A and B will be

  1. 90
  2. 120
  3. 0
  4. 60
AIPMT 2001
10

Two particles having mass M and m are moving in a circular path having radius R and r. If their time periods are the same, then the ratio of their angular velocities will be

  1. rR
  2. Rr
  3. 1
  4. Rr
AIPMT 2001
11

A particle is projected making an angle of 45 with horizontal having kinetic energy K. The kinetic energy at highest point will be

  1. K 2
  2. K2
  3. 2K
  4. K
AIPMT 2001

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