A satellite moves around the earth in a circular orbit of radius R making one revolution per day. A second satellite moving in a circular orbit moves around the earth once in 8 days. The radius of the orbit of the second satellite is

Question

A satellite moves around the earth in a circular orbit of radius R making one revolution per day. A second satellite moving in a circular orbit moves around the earth once in 8 days. The radius of the orbit of the second satellite is (A) 8R (B) 4R (C) 2R (D) R

Tardigrade Admin · Accepted Answer

Given that, T1 = 1 day and T2 = 8 days â´ (T2/T1) = (. (r2/r1) .)3 / 2 ⇒ (r2/r1) = (. (T2/T1) .)2 / 3 = (. (8/1) .)2 / 3 = 4 ⇒ r2 = 4 r1 = 4 R

Q. A satellite moves around the earth in a circular orbit of radius $R$ making one revolution per day. A second satellite moving in a circular orbit moves around the earth once in $8$ days. The radius of the orbit of the second satellite is

$8 R$

$4 R$

$2 R$

$R$

Given that, $T_{1} = 1$ day and $T_{2} =$ 8 days
∴ $\frac{T _{2}}{T _{1}} = (\frac{r _{2}}{r _{1}})^{3/2}$ $\Rightarrow$ $\frac{r _{2}}{r _{1}} = (\frac{T _{2}}{T _{1}})^{2/3} = (\frac{8}{1})^{2/3} = 4$ $\Rightarrow$ $r_{2} = 4 r_{1} = 4 R$

Q. A satellite moves around the earth in a circular orbit of radius R making one revolution per day. A second satellite moving in a circular orbit moves around the earth once in 8 days. The radius of the orbit of the second satellite is

8R

4R

2R

R

Given that, T1​=1 day and T2​= 8 days ∴ T1​T2​​=(r1​r2​​)3/2 ⇒ r1​r2​​=(T1​T2​​)2/3=(18​)2/3=4 ⇒ r2​=4r1​=4R

Q. A satellite moves around the earth in a circular orbit of radius $R$ making one revolution per day. A second satellite moving in a circular orbit moves around the earth once in $8$ days. The radius of the orbit of the second satellite is

$8 R$

$4 R$

$2 R$

$R$

Given that, $T_{1} = 1$ day and $T_{2} =$ 8 days
∴ $\frac{T _{2}}{T _{1}} = (\frac{r _{2}}{r _{1}})^{3/2}$ $\Rightarrow$ $\frac{r _{2}}{r _{1}} = (\frac{T _{2}}{T _{1}})^{2/3} = (\frac{8}{1})^{2/3} = 4$ $\Rightarrow$ $r_{2} = 4 r_{1} = 4 R$