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

Question

Two cars of masses m1 , and m2 are moving in circles of radii r1 and r2, respectively. Their speeds are such that they make complete circles in the same time t. The ratio of their centripetal acceleration is (A) m1r1: m2r2 (B) m1: m2 (C) r1: r2 (D)  1: 1

Tardigrade Admin · Accepted Answer

Centripetal acceleration, ae=ω2r Angular velocity , ω=(2 π/T) The cars make complete circle in same time. As T1=T2 ⇒ ω1=ω2 ∴ (ac1/ac2)=(r1/r2)

Q. Two cars of masses $m_{1}$ , and $m_{2}$ are moving in circles of radii $r_{1}$ and $r_{2}$ , respectively. Their speeds are such that they make complete circles in the same time $t$ . The ratio of their centripetal acceleration is

$m_{1} r_{1} : m_{2} r_{2}$

$m_{1} : m_{2}$

$r_{1} : r_{2}$

$1 : 1$

Centripetal acceleration, $a_{e} = ω^{2} r$
Angular velocity , $ω = \frac{2 π}{T}$
The cars make complete circle in same time.
As $T_{1} = T_{2}$
$\Rightarrow ω_{1} = ω_{2}$
$∴ \frac{a _{c_{1}}}{a _{c_{2}}} = \frac{r _{1}}{r _{2}}$

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

m1​r1​:m2​r2​

m1​:m2​

r1​:r2​

1:1