A particle of mass 3.6 x 10 ^ -6 kg revolving around the earth has a radial acceleration of 4.3 x 10 ^7 ms ^…

Analyze the question We are given the mass and the radial (centripetal) acceleration, and we need the centripetal force.

Concept Centripetal force is given by Newton's second law applied to circular motion:

F = m × a

where a is the radial (centripetal) acceleration.

Solution

• m = 3.6 × 10⁻⁶ kg
• a = 4.3 × 10⁷ m/s²

F = (3.6 × 10⁻⁶) × (4.3 × 10⁷) F = (3.6 × 4.3) × 10^(−6+7) F = 15.48 × 10¹ F = 154.8 N ≈ 1.55 × 10² N

Answer

Tip When multiplying numbers in standard form, multiply the coefficients and add the powers of 10. Here 3.6 × 4.3 = 15.48 and the powers give 10¹, so the answer is about 155 N. Also, if a question gives mass and acceleration, you don't need the radius or speed. Just use F = ma.