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

Work Energy and Power question

2016 · Q145
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. /Work Energy and Power
  5. /2016 · Q145

Work Energy and Power question

2016 · Q145

NEETPhysicsWork Energy and PowerMCQ+4 / −1
A body of mass 1 kg begins to move under the action of a time dependent force F→=(2ti^+3t2J^)N,\overrightarrow F = \left( {2t\widehat i + 3{t^2}\widehat J} \right)N,F=(2ti+3t2J)N, where i^{\widehat i}i and j^{\widehat j}j​ are unit vectors along x and y axis. What power will be developed by the force at the time t ?
  1. A
    (2t3 + 3t4) W
  2. B
    (2t3 + 3t5) W
  3. C
    (2t2 + 3t3) W
  4. D
    (2t2 + 4t4) W
View written solutionFree

Correct answer: B

Given force (F→)=2ti^+3t2j^(\overrightarrow F) = 2t\widehat i + 3{t^2}\widehat j(F)=2ti+3t2j​

According to Newton's second law of motion,

mdv→dt=2ti^+3t2j^  (m=1kg)m{{d\overrightarrow v } \over {dt}} = 2t\widehat i + 3{t^2}\widehat j\,\,(m = 1kg)mdtdv​=2ti+3t2j​(m=1kg)

⇒∫0v→dv→=∫0t(2ti^+3t2j^)dt \Rightarrow \int\limits_0^{\overrightarrow v } {d\overrightarrow v } = \int\limits_0^t {\left( {2t\widehat i + 3{t^2}\widehat j} \right)} dt⇒0∫v​dv=0∫t​(2ti+3t2j​)dt

⇒v=t2i^+t3j^ \Rightarrow v = {t^2}\widehat i + {t^3}\widehat j⇒v=t2i+t3j​

Power (P) = F→.v→(2ti^+3t2j^)(t2i^+t3j^)\overrightarrow F .\overrightarrow v \left( {2t\widehat i + 3{t^2}\widehat j} \right)\left( {{t^2}\widehat i + {t^3}\widehat j} \right)F.v(2ti+3t2j​)(t2i+t3j​)

= (2t3 + 3t5)W

PreviousNext

More from Work Energy and Power

  • What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop?2016 · MCQ
  • A particle moves from a point (−2i+5j​) to (4j​+3k) when a force of (4i+3j​) N is applied. How much work has been done by…2016 · MCQ
  • Two particles A and B, move with constant velocities v1​​ and v2​​. At the initial moment their position vectors are r1​​ and r2​​…2015 · MCQ
  • A ball is thrown vertically downwards from a height of 20 m with an initial velocity v0. It collides with the ground, losses 50 percent of its energy in collision and rebounds to the same height. The initial velocity v0 is (Take g = 10 m s−…2015 · MCQ
  • The heart of a man pumps 5 litres of blood through the arteries per minute at a pressure of 150 mm of mercury. If the density of mercury be 13.6 × 103 kg/m3 and g = 10 m/s2 then the power (in watt) is2015 · MCQ
  • On a frictionless surface, a block of mass M moving at speed v collides elastically with another block of same mass M which is initially at rest. After collision the first block moves at an angle θ to its initial direction and has…2015 · MCQ
  • A block of mass 10 kg, moving in x direction with a constant speed of 10 m s−1, is subjected to a retarding force F = 0.1x J/m during its travel from x = 20 m to 30 m. Its final KE will be2015 · MCQ
  • A particle of mass m is driven by a machine that delivers a constant power k watts. If the particle starts from rest the force on the particle at time t is2015 · MCQ