Correct Answer - Option 2 : 2 ms
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Concept:
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Kinetic energy (K.E): The energy possessed by a body by the virtue of its motion is called kinetic energy.
The expression for kinetic energy is given by:
\(KE = \frac{1}{2}m{v^2}\)
Where m = mass of the body and v = velocity of the body
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Momentum (p): The product of mass and velocity is called momentum.
Momentum (p) = mass (m) × velocity (v)
The relationship between the kinetic energy (KE or k) and Linear momentum is given by:
As we know,
\(KE = \frac{1}{2}m{v^2}\)
Divide numerator and denominator by m, we get
\(KE = \frac{1}{2}\frac{{{m^2}{v^2}}}{m} = \frac{1}{2}\frac{{\;{{\left( {mv} \right)}^2}}}{m} = \frac{1}{2}\frac{{{p^2}}}{m}\;\) [p = mv]
\(\therefore KE = \frac{1}{2}\frac{{{p^2}}}{m}\;\)
\(p = \sqrt {2mKE} \)
Calculation:
Let, m be the mass of the body and v be the velocity of the body.
Now, momentum of the body is
p = mv
Kinetic energy is
\(KE = \frac{1}{2}m{v^2}\)
As per given condition,
Say,
\(Momentum = Kinetic\;energy = x\)
\(\Rightarrow mv= {1\over2}mv^2=x\)
\(\Rightarrow {1\over2}mv^2=x\)
\(\Rightarrow {1\over2m}m^2v^2=x\)
we know (mv)2 = x2
\(\Rightarrow {1\over2m}x^2=x\)
\(\Rightarrow x=2m\)
\(\Rightarrow mv=2m \Rightarrow v=2\)
Hence the correct answer is 2 m/s.
