JEE Main 2024 · 1 February · evening · Single correct · +4 / −1
A body of mass 4 kg experiences two forces F⃗₁=5 î+8 ĵ+7 k̂ and F⃗₂=3 î-4 ĵ-3 k̂. The acceleration acting on the body is :
- (a) 2 î+ĵ+k̂
- (b) 4 î+2 ĵ+2 k̂
- (c) -2 î-ĵ-k̂
- (d) 2 î+3 ĵ+3 k̂
Answer and solution
Answer (a) 2 î+ĵ+k̂
Solution
Physics sir · 3 steps
Add the two forces component by component first, then divide that net force by the mass.
- Net force. Newton's second law uses the net force. Add the î, ĵ and k̂ parts separately, keeping the minus signs.
F⃗ = (5+3)î + (8-4)ĵ + (7-3)k̂ = 8î + 4ĵ + 4k̂ N
- Divide by mass. a⃗ = F⃗/m = (8î + 4ĵ + 4k̂)/4. Every component is divided by 4.
- So. a⃗ = 2î + ĵ + k̂ m s⁻², which is option (a).
The idea to keep. With vector forces, find the resultant one component at a time, then use a⃗ = F⃗ₙₑₜ/m. The acceleration always points along the net force.
Answer from the NTA final answer key. Solution by PrepWiser.