The displacement of a particle of mass 3 g executing simple harmonic motion is given by Y=3 sin (0.2 t) in SI units. The kinetic energy of the particle at a point which is at a distance equal to (1/3) of its amplitude from its mean position is

Question

The displacement of a particle of mass 3 g executing simple harmonic motion is given by Y=3 sin (0.2 t) in SI units. The kinetic energy of the particle at a point which is at a distance equal to (1/3) of its amplitude from its mean position is (A)  12× 103J  (B)  25× 10-3J  (C)  0.48× 10-3J  (D)  0.24× 10-3J

Tardigrade Admin · Accepted Answer

Equation of SHM , Y=3 sin (0.2 t ) Comparing with Y=a sin ω t, we have a=3 m, ω=0.2 s-1 Mass of the particle =3 g =3 × 10-3 kg Therefore, kinetic energy of the particle is K=(1/2) m ω-3(a2-x2) =(1/2) × 3 × 10-3 ×(0.2)2(32-12) (∵ x=(1/3)) =0.48 × 10-3 J

Q. The displacement of a particle of mass $3 g$ executing simple harmonic motion is given by $Y = 3 sin (0.2 t)$ in $S I$ units. The kinetic energy of the particle at a point which is at a distance equal to $\frac{1}{3}$ of its amplitude from its mean position is

$12 \times 1 0^{3} J$

$25 \times 1 0^{- 3} J$

$0.48 \times 1 0^{- 3} J$

$0.24 \times 1 0^{- 3} J$

Q. The displacement of a particle of mass 3g executing simple harmonic motion is given by Y=3sin(0.2t) in SI units. The kinetic energy of the particle at a point which is at a distance equal to 31​ of its amplitude from its mean position is

12×103J

25×10−3J

0.48×10−3J

0.24×10−3J

Equation of SHM,Y=3sin(0.2t) Comparing with Y=asinωt, we have a=3m,ω=0.2s−1 Mass of the particle =3g=3×10−3kg Therefore, kinetic energy of the particle is K=21​mω−3(a2−x2) =21​×3×10−3×(0.2)2(32−12) (∵x=31​) =0.48×10−3J

Q. The displacement of a particle of mass $3 g$ executing simple harmonic motion is given by $Y = 3 sin (0.2 t)$ in $S I$ units. The kinetic energy of the particle at a point which is at a distance equal to $\frac{1}{3}$ of its amplitude from its mean position is

$12 \times 1 0^{3} J$

$25 \times 1 0^{- 3} J$

$0.48 \times 1 0^{- 3} J$

$0.24 \times 1 0^{- 3} J$