Question

A particle is moving with constant speed in a circular path. When the particle turns by an angle $90\degree$ , the ratio of instantaneous velocity to its average velocity is $π : x\sqrt2$. The value of x will be -

• A. 7
• B. 2
• C. 1
• D. 5

Answer 1

Answer: (B)

2

Answer 2

V_𝐴 = 𝑣𝑗̂ And 𝑉_𝐵 = −𝑣𝑖̂ Time to reach from A to B = 2𝜋𝑅 4 × 1 𝑣 = 𝜋𝑅 2𝑣 Displacement from A to B = 𝑅√2 Now, Average velocity from A to B = 𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡/ 𝑇𝑖𝑚𝑒 = 𝑅√2/ 𝜋𝑅/ 2𝑣 = 2√2𝑣/ 𝜋 Instantaneous velocity at B is −𝑣𝑖̂ According to question, 𝑖𝑛𝑠𝑡𝑎𝑛𝑡𝑎𝑛𝑒𝑜𝑢𝑠 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦/ 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 = 𝜋 /𝑥√2 𝑣/ 2√2𝑣/ 𝜋 = 𝜋/ 𝑥√2 ⟹ 𝜋/ 2√2 = 𝜋/ 𝑥√2 ⟹ 𝑥 = 2