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A particle is moving along a circle such that itsposition vector with respect to origin isr = 2r° (sinwti^ + coswtj^), where r° and w areconstant. The motion is with(1) Constant speed 12) Constant velocity43) Constant acceleration 14) Constant momentum​

Answer»

ANSWER : option (1) constant speed

explanation : A PARTICLE moves along a circle such that its position vector with respect to origin is r=2r_0(sin\omega t\hat{i}+cos\omega t\hat{<klux>J</klux>})

where r and ω are constants.

differentiating with respect to time,

dr/dt = 2r_0[d(sinωt)/dt i + d(cosωt)/dt j ]

= 2r_0(-ωcosωt i + ωsinωt j)

= 2r_0\omega(-cosωt i + sinωt j)

so, velocity of particle is v = dr/dt = 2r_0\omega(-cosωt i + sinωt j)

now, speed of particle = |v|

= 2r_0\omega\sqrt{sin^2(\omega t)+cos^2(\omega t)}

= 2r_0\omega (constant )

hence, it is CLEAR that speed of particle is constant.

hence, option (1) is correct choice



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