Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Motion in A Plane question

2021 · Q168
Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.
  1. PYQ Library
  2. /NEET
  3. /Physics
  4. /Motion in A Plane
  5. /2021 · Q168

Motion in A Plane question

2021 · Q168

NEETPhysicsMotion in A PlaneMCQ+4 / −1
A particle moving in a circle of radius R with a uniform speed takes a time T to complete one revolution.

If this particle were projected with the same speed at an angle 'θ\thetaθ' to the horizontal, the maximum height attained by it equals 4R. The angle of projection, θ\thetaθ, is then given by :
  1. A
    θ=sin⁡−1(2gT2π2R)1/2\theta = {\sin ^{ - 1}}{\left( {{{2g{T^2}} \over {{\pi ^2}R}}} \right)^{1/2}}θ=sin−1(π2R2gT2​)1/2
  2. B
    θ=cos⁡−1(gT2π2R)1/2\theta = {\cos ^{ - 1}}{\left( {{{g{T^2}} \over {{\pi ^2}R}}} \right)^{1/2}}θ=cos−1(π2RgT2​)1/2
  3. C
    θ=cos⁡−1(π2RgT2)1/2\theta = {\cos ^{ - 1}}{\left( {{{{\pi ^2}R} \over {g{T^2}}}} \right)^{1/2}}θ=cos−1(gT2π2R​)1/2
  4. D
    θ=sin⁡−1(π2RgT2)1/2\theta = {\sin ^{ - 1}}{\left( {{{{\pi ^2}R} \over {g{T^2}}}} \right)^{1/2}}θ=sin−1(gT2π2R​)1/2
View written solutionFree

Correct answer: A

T=2πRVT = {{2\pi R} \over V}T=V2πR​

V=2πRTV = {{2\pi R} \over T}V=T2πR​

H=u2sin⁡2θ2gH = {{{u^2}{{\sin }^2}\theta } \over {2g}}H=2gu2sin2θ​

4R=4π2R2sin⁡2θT22g4R = {{4{\pi ^2}{R^2}{{\sin }^2}\theta } \over {{T^2}2g}}4R=T22g4π2R2sin2θ​

sin⁡2θ=8RT2g4π2R2{\sin ^2}\theta = {{8R{T^2}g} \over {4{\pi ^2}{R^2}}}sin2θ=4π2R28RT2g​

sin⁡2θ=2T2gπ2R{\sin ^2}\theta = \sqrt {{{2{T^2}g} \over {{\pi ^2}R}}} sin2θ=π2R2T2g​​

θ=sin⁡−1(2T2gπ2R)1/2\theta = {\sin ^{ - 1}}{\left( {{{2{T^2}g} \over {{\pi ^2}R}}} \right)^{1/2}}θ=sin−1(π2R2T2g​)1/2

PreviousNext

More from Motion in A Plane

  • A car starts from rest and accelerates at 5m/s2. At t = 4 s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at t = 6 s? (Take g = 10 m/s2)2021 · MCQ
  • When an object is shot from the bottom of a long smooth inclined plane kept at an angle 60o with horizontal, it can travel a distance x1 along the plane. But when the inclination is decreased to 30o and the same object is shot with the…2019 · MCQ
  • A particle moving with velocity V is acted by three forces shown by the vector triangle PQR. The velocity of the particle will : Includes diagram2019 · MCQ
  • The x and y coordinates of the particle at any time are x = 5t − 2t2 and y = 10t respectively, where x and y are in metres and t in seconds. The acceleration of the particle at t = 2 s is2017 · MCQ
  • If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is2016 · MCQ
  • A particle moves so that its position vector is given by r=cosωtx+sinωty​, where ω is a constant. Which of the following is true?2016 · MCQ
  • In the given figure, a = 15 m s−2 represents the total acceleration of particle moving in the clockwise direction in a circle of radius R = 2.5 m at a given instant of time. The speed of the particle is Includes diagram2016 · MCQ
  • If vectors A=cosωti+sinωtj​ and B=cos2ωt​i+sin2ωt​j​ are functions of time, then the value of t at which…2015 · MCQ