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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Motion in Two Dimensions

NTA Abhyas 2020 · Physics · Motion in Two Dimensions

A particle of mass m is projected at an angle of 60^ o with a...

A particle of mass m is projected at an angle of 60^{o} with a velocity of 20 m/s relative to the ground from a plank of same mass m which is placed on a smooth surface initially plank was at rest. The minimum length of the plank for which the ball will fall on the plank itself is

A particle of mass m is projected at an angle of 60^ o with a velocity of 20 m/s relative to the ground from a plank of

Options

  1. A403m4 0 \sqrt{3} \text{m}
  2. B203m2 0 \sqrt{3} \text{m}
  3. C103m1 0 \sqrt{3} \text{m}
  4. D603m6 0 \sqrt{3} \text{m}

Correct answer

A. 403m4 0 \sqrt{3} \text{m}

Step-by-step solution



A particle of mass m is projected at an angle of 60^ o with a velocity of 20 m/s relative to the ground from a plank of

Since theexternalforceonthesystemiszero,locationofCOMwillnotshift.theexternalforceonthesystemiszero, locationofCOMwillnotshift.

⇒m1x1=m2x2⇒ {m}_{1}{x}_{1} = {m}_{2}{x}_{2}

mx=m(L−x)mx = m \left(L - x\right)

⇒x=L2⇒ x = \dfrac{L}{2}

soplankwillshiftbyL2soplankwillshiftby\dfrac{L}{2} towardsleft.<br/><br/><br /><br />NowrangeRshouldbe\mathop{< }_{_}\dfrac{ L}{2}

⇒L=2R⇒ L = 2R

⇒L=2u2sin⁡30g=⇒ L = 2\dfrac{u^{2}\sin 30}{g} ==40\sqrt{3}$$
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