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 Power and Energy question

2023 · 1 Feb · Shift 1 · Q67
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. /JEE Main
  3. /Physics
  4. /Work Power and Energy
  5. /2023 · 1 Feb · Shift 1 · Q67

Work Power and Energy question

2023 · 1 Feb · Shift 1 · Q67

JEE MainPhysicsWork Power and EnergyNumerical+4 / −1
A small particle moves to position 5i^−2j^+k^5 \hat{i}-2 \hat{j}+\hat{k}5i^−2j^​+k^ from its initial position 2i^+3j^−4k^2 \hat{i}+3 \hat{j}-4 \hat{k}2i^+3j^​−4k^ under the action of force 5i^+2j^+7k^ N5 \hat{i}+2 \hat{j}+7 \hat{k} \mathrm{~N}5i^+2j^​+7k^ N. The value of work done will be ‾\underline{\hspace{2cm}}​ J.
Numerical answer
View written solutionFree

Correct answer: 40

  1. Given:

    • Initial position: r⃗i=2i^+3j^−4k^\vec r_i = 2\hat i + 3\hat j - 4\hat kri​=2i^+3j^​−4k^
    • Final position: r⃗f=5i^−2j^+k^\vec r_f = 5\hat i - 2\hat j + \hat krf​=5i^−2j^​+k^
    • Force: F⃗=5i^+2j^+7k^ N\vec F = 5\hat i + 2\hat j + 7\hat k\,\text{N}F=5i^+2j^​+7k^N

  2. Find displacement: Δr⃗=r⃗f−r⃗i\Delta \vec r = \vec r_f - \vec r_iΔr=rf​−ri​ =(5−2)i^+(−2−3)j^+(1−(−4))k^= (5-2)\hat i + (-2-3)\hat j + \left(1-(-4)\right)\hat k=(5−2)i^+(−2−3)j^​+(1−(−4))k^ =3i^−5j^+5k^= 3\hat i - 5\hat j + 5\hat k=3i^−5j^​+5k^

  3. Work done by a constant force: W=F⃗⋅Δr⃗W = \vec F \cdot \Delta \vec rW=F⋅Δr

  4. Compute the dot product: W=(5i^+2j^+7k^)⋅(3i^−5j^+5k^)W = (5\hat i + 2\hat j + 7\hat k) \cdot (3\hat i - 5\hat j + 5\hat k)W=(5i^+2j^​+7k^)⋅(3i^−5j^​+5k^) =5⋅3+2⋅(−5)+7⋅5= 5\cdot 3 + 2\cdot(-5) + 7\cdot 5=5⋅3+2⋅(−5)+7⋅5 =15−10+35= 15 - 10 + 35=15−10+35 =40 J= 40\,\text{J}=40J

  5. Final answer: 40\boxed{40}40​

The derived answer matches the stored correct answer.

PreviousNext

More from Work Power and Energy

  • A block is fastened to a horizontal spring. The block is pulled to a distance x=10 cm from its equilibrium position (at x=0) on a frictionless surface from rest. The energy of the block at x=5cm is 0.25 J…2023 · Numerical
  • A force F=(5+3y2) acts on a particle in the y-direction, where F is in newton and y is in meter. The work done by the force during a displacement from y=2 m to y=5 m is ​…2023 · Numerical
  • A particle of mass 10 g moves in a straight line with retardation 2x, where x is the displacement in SI units. Its loss of kinetic energy for above displacement is (x10​)−n J. The value of n…2023 · Numerical
  • A body is dropped on ground from a height 'h1​' and after hitting the ground, it rebounds to a height 'h2​'. If the ratio of velocities of the body just before and after hitting ground is 4 , then percentage loss in kinetic energy…2023 · Numerical
  • A bullet of mass 0.1 kg moving horizontally with speed 400 ms−1 hits a wooden block of mass 3.9 kg kept on a horizontal rough surface. The bullet gets embedded into the block and moves $20…2023 · MCQ
  • A body of mass 5 kg is moving with a momentum of 10 kg ms−1. Now a force of 2 N acts on the body in the direction of its motion for 5 s. The increase in the Kinetic energy of the…2023 · Numerical
  • A closed circular tube of average radius 15 cm, whose inner walls are rough, is kept in vertical plane. A block of mass 1 kg just fit inside the tube. The speed of block is 22 m/s, when it is introduced at the top of tube. After completing… Includes diagram2023 · Numerical
  • If the maximum load carried by an elevator is 1400 kg(600 kg- Passengers + 800 kg- elevator), which is moving up with a uniform speed of 3 m s−1 and the frictional force acting on…2023 · Numerical