A particle of mass 1 kg is at origin. At t = 0. It is given a velocity of 1m/s at angle of 30° with y-axis in x-y plane. It is moved under the influence of a force 𝐅 = 𝐕 × 𝐀, where 𝐀 is constant vector of magnitude π units directed along positive x-axis. The x-coordinate of particle at t = 2s is: ______ m (𝐕 - instantaneous velocity)
Physics · Mixed Chapter
JEE Mains

Question

A particle of mass 1 kg is at origin. At t = 0. It is given a velocity of 1m/s at angle of 30° with y-axis in x-y plane. It is moved under the influence of a force 𝐅 = 𝐕 × 𝐀, where 𝐀 is constant vector of magnitude π units directed along positive x-axis. The x-coordinate of particle at t = 2s is: ______ m (𝐕 - instantaneous velocity)

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: F=v×A with A directed along +x. The cross product is perpendicular to A, so the x-component of force vanishes: Fₓ=0. Step 2: By Newton's second law, aₓ=Fₓ/m=0. Consequently the initial horizontal velocity remains unchanged. Step 3: Initial speed is 1 m/s at 30° to the y-axis, giving vₓ=1 sin30°=½ m/s. Step 4: Starting at x=0, x(2s)=vₓ×2=1 m. Answer: 1.