Two particles of masses 3.4 kg and 2.5 kg have initial speeds 5 m·s⁻¹ and 12 m·s⁻¹, respectively, and move with constant accelerations. During the 5th second, they cover 104 m and 129 m, respectively. After 10 s, their momentum ratio p₁ ÷ p₂ is x ÷ 8. Find x.
Physics · Center of maas , Momentum and Collision · momentum and conservation of momentum
JEE Mains 2026 8 April Evening Shift

Question

Two particles of masses 3.4 kg and 2.5 kg have initial speeds 5 m·s⁻¹ and 12 m·s⁻¹, respectively, and move with constant accelerations. During the 5th second, they cover 104 m and 129 m, respectively. After 10 s, their momentum ratio p₁ ÷ p₂ is x ÷ 8. Find x.

Physics · Center of maas , Momentum and Collision · momentum and conservation of momentum

JEE Mains 2026 8 April Evening Shift

G1 Physics · Accepted Answer

For uniformly accelerated motion, the distance covered during the nth second is sₙ = u + (a ÷ 2)(2n-1). For the first particle: n = 5, u₁ = 5 m·s⁻¹, s₅ = 104 m. Therefore, 104 = 5 + (a₁ ÷ 2)(9). Thus, 99 = 9a₁ ÷ 2, so a₁ = 22 m·s⁻². For the second particle: u₂ = 12 m·s⁻¹, s₅ = 129 m. Hence, 129 = 12 + (a₂ ÷ 2)(9). Thus, 117 = 9a₂ ÷ 2, so a₂ = 26 m·s⁻². After 10 s, their speeds are v₁ = u₁+a₁t = 5+22×10 = 225 m·s⁻¹, and v₂ = 12+26×10 = 272 m·s⁻¹. Their momenta are p₁ = 3.4×225, p₂ = 2.5×272. The…