Question

Two cars of mass m₁ and m₂ are moving in circles of radii r₁ and r₂, respectively. Their speeds are such that they make complete circles at the same time t. The ratio of their centripetal acceleration is:

Options

• m₁r₂ : m₂r₂

• m₁ : m₂

• r₁ : r₂

• 1:1

Answer 1

r₁ : r₂

Explanation:

`"a"_1 = "v"_1^2/"r"_1`  ..........(1)

`"a"_2 = "v"_2^2/"r"_2`  ...........(2)

t₁ = `(2π"r"_1)/"v"_1` and t₂ =  `(2π"r"_2)/"v"_2`

⇒ Putting v₁ and v₂ in equations (1) and (2) in terms of t.

`"a"_1 = (4π^2"r"_1)/"t" ; "a"_2 = (4π^2"r"_2)/"t"`

Now, `"a"_1/"a"_2 = "r"_1/"r"_2`