A body of mass 2kg is projected with a speed 4m/s at an angle 45∘ to the horizontal. What will be its angular momentum about the point of projection when the body is at the highest point in its trajectory?
A
1.6√2kg m2/s
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B
32.6√2kg m2/s
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C
16√2kg m2/s
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D
3.26√2kg m2/s
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Solution
The correct option is D3.26√2kg m2/s
For given projectile motion, Range (R)=u2sin2θg=42sin(2×45∘)9.8=169.8m Maximum height (Hmax)=u2sin2θ2g=49.8m So at maximum height, →r=x^i+y^j=R2^i+Hmax^j=(89.8^i+49.8^j)m and we know that at highest point velocity will be in x direction only, →u=ux^i+uy^j=ucosθ^i+0^j=4cos45∘^i+0^j=(4√2^i+0^j)m/s Now we know, Angular momentum about origin (→L)=→r×→p =→r×(m→u)=m(→r×→u)=2[(89.8^i+49.8^j)×(4√2^i+0^j)]=2×4×49.8×√2(^j×^i) =3.26√2(−^k) as, (^j×^i=−^k) |L|=3.26√2kg m2/s Hence, option (d) is the correct answer.