Motion in A Plane

More Topic from Physics

Question 1

If space straight A with rightwards arrow on top space straight x space straight B with rightwards arrow on top space equals space straight B with rightwards arrow on top space straight x space straight A with rightwards arrow on top then the angle between A and B isπ
  • π

  • π/3

  • π/2

  • π/4

Solution

A.

π

open parentheses straight A with rightwards arrow on top space straight x space straight B with rightwards arrow on top close parentheses space equals space left parenthesis straight B with rightwards arrow on top space straight x straight A with rightwards arrow on top right parenthesis
rightwards double arrow space open parentheses straight A with rightwards arrow on top space straight x space straight B with rightwards arrow on top close parentheses minus space left parenthesis straight B with rightwards arrow on top space straight x straight A with rightwards arrow on top right parenthesis space equals space 0
rightwards double arrow space open parentheses straight A with rightwards arrow on top space straight x space straight B with rightwards arrow on top close parentheses plus space left parenthesis straight B with rightwards arrow on top space straight x straight A with rightwards arrow on top right parenthesis space equals space 0
open square brackets therefore space left parenthesis straight B with rightwards arrow on top space straight x space straight A with rightwards arrow on top right parenthesis space equals space minus space left parenthesis straight A with rightwards arrow on top space straight x space straight B with rightwards arrow on top right parenthesis close square brackets
2 space open parentheses straight A with rightwards arrow on top space straight x space straight B with rightwards arrow on top close parentheses space equals 0
rightwards double arrow space space 2 AB space sin space straight theta space equals space 0
sin space straight theta space equals space 0 space space left square bracket space because space vertical line straight A with rightwards arrow on top vertical line space equals space straight A space not equal to 0 comma space vertical line straight B with rightwards arrow on top vertical line space equals space straight B not equal to space 0 right square bracket
straight theta space equals space 0 space or space straight pi space
Question 2

A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10,000. N/m. The spring compresses by

  • 5.5 cmYes

  • 2.5 cm

  • 11 cm

  • 3.5 cm

Solution

A.

5.5 cmYes

Question 3

A body is at rest at x = 0. At t = 0, it starts moving in the positive x-direction with a constant acceleration. At the same instant another body passes through x = 0 moving in the positive x-directionn with a constant speed. The position of the first body is given by x1(t) after time ‘t’ and that of the second body by x2(t) after the same time interval. Which of the following graphs correctly describes (x1 – x2)as a function of time ‘t’?

Solution

B.

straight x subscript 1 space left parenthesis straight t right parenthesis space equals space 1 half space at squared
straight x subscript 2 space left parenthesis straight t right parenthesis space equals space vt
straight x subscript 1 minus straight x subscript 2 space equals space 1 half at squared space minus vt
Question 4

A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time?

Solution

A.

Velocity at any time t is given by

v = u + at

v = v0 + (–g)t
v = v0 – gt

Straight line negative slope.

Question 5

A body of mass m = 10–2 kg is moving in a medium and experiences a frictional force F = –kv2. Its initial speed is v0 = 10 ms–1. If, after 10 s, its energy is 1/8 mv02,the value of k will be

  • 10-4 kg m-1

  • 10–1 kg m–1 s–1

  • 10-3 kg m-1

  • 10-3 kg s-1

Solution

A.

10-4 kg m-1

1 half mv subscript straight f superscript 2 space equals space 1 over 8 mv subscript 0 superscript 2
straight v subscript straight f space equals space straight v subscript 0 over 2 space equals space 5 space straight m divided by straight s
left parenthesis 10 to the power of negative 2 end exponent right parenthesis space dv over dt space equals space minus space kv squared
integral subscript 10 superscript 5 space dv over straight v squared space equals negative 100 space straight k integral subscript 0 superscript 10 space dt
1 fifth space minus space 1 over 10 space equals space 100 space straight k space left parenthesis 10 right parenthesis
straight k space equals space 10 to the power of negative 4 end exponent
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