JEE Mains · Physics · STD 11 - Motion in plane
- JEE Mains 2021
- Hard
- Numerical
The projectile motion of a particle of mass \(5\, g\) is shown in the figure. The initial velocity of the particle is \(5 \sqrt{2}\, ms ^{-1}\) and the air resistance is assumed to be negligible. The magnitude of the change in momentum between the points \(A\) and \(B\) is \(x \times 10^{-2}\, kgms ^{-1} .\) The value of \(x ,\) to the nearest integer, is ...... .
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) \(5\)
Step-by-step Solution
Detailed explanation
\(|\overrightarrow{ u }|=|\overrightarrow{ v }|.....(1)\)
\(\overrightarrow{ u }=u \cos 45 \hat{ i }+ u \sin 45 \hat{ j }.....(2)\)
\(\overrightarrow{ v }= v \cos 45 \hat{ i }- v \sin 45 \hat{ j }.....(3)\)
\(|\overrightarrow{\Delta P }|=| m (\overrightarrow{ v }-\overrightarrow{ u })|.....(4)\)
\(\Delta P =2 mu \sin 45^{\circ}\)
\(=2 \times 5 \times 10^{-3} \times 5 \sqrt{2} \times \frac{1}{\sqrt{2}}\)
\(=50 \times 10^{-3}\)
\(=5 \times 10^{-2}\)
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