You visited us 1 times! Enjoying our articles? Unlock Full Access!

Gravitational Field Due to a Solid Sphere

The magnitude...

Question

The magnitudes of the gravitational force at distances $r_{1}$ and $r_{2}$ from the centre of a uniform sphere of radius $R$ and mass $M$ are $F_{1}$ and $F_{2}$ respectively. Then

\frac{F_{1}}{F_{2}} = \frac{r_{1}}{r_{2}}

r_{1} < R

and

r_{2} < R

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{F_{1}}{F_{2}} = \frac{r_{1}^{2}}{r_{2}^{2}}

r_{1} < R

and

r_{2} < R

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{F_{1}}{F_{2}} = \frac{r_{1}}{r_{2}}

r_{1} > R

and

r_{2} > R

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{F_{1}}{F_{2}} = \frac{r_{2}^{2}}{r_{1}^{2}}

r_{1} < R

and

r_{2} < R

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\frac{F_{1}}{F_{2}} = \frac{r_{1}}{r_{2}}$ if $r_{1} < R$ and $r_{2} < R$
For $r < R$
$g = \frac{4}{3} π ρ G r ∴ g \propto r$

For $r > R$
$g = \frac{G M}{r^{2}} ∴ g \propto \frac{1}{r^{2}}$

If $r_{1} < R$ and $r_{2} < R$ then $\frac{F_{1}}{F_{2}} = \frac{g_{1}}{g_{2}} = \frac{r_{1}}{r_{2}}$

If $r_{1} > R and r_{2} > R$ then $\frac{F_{1}}{F_{2}} = \frac{g_{1}}{g_{2}} = {(\frac{r_{2}}{r_{1}})}^{2}$

Suggest Corrections

Similar questions

The magnitude of the gravitational force at distance $r_{1}$ and $r_{2}$ from the centre of a uniform sphere of radius R and mass M are $F_{1}$ and $F_{2}$ respectively. Then,

If the sum of the areas of two circles with radii $R_{1}$ and $R_{2}$ is equal to the area of a circle of radius R then

(a) $R_{1} + R_{2} = R$

(b) $R_{1} + R_{2} > R$

(d) $R_{1}^{2} + R_{2}^{2} = R^{2}$

Q. The magnitudes of the gravitational force at distances

r_{1}

and

r_{2}

from the centre of a uniform sphere of radius R and mass M are

F_{1}

and

F_{2}

respectively. Then

If the sum of the areas of two circles with radii R₁ and R₂ is equal to the area of a circle of radius R, then

Q. If the sum of the areas of two circles with radii R₁ and R₂ is equal to the area of a circle of radius R, then
(a)

R_{1} + R_{2} = R

(b)

R_{1} + R_{2} < R

(c)

R_{1}^{2} + R_{2}^{2} < R^{2}

(d)

R_{1}^{2} + R_{2}^{2} = R^{2}

Join BYJU'S Learning Program

The magnitudes of the gravitational force at distances r1 and r2 from the centre of a uniform sphere of radius R and mass M are F1 and F2 respectively. Then

The correct option is A F1F2=r1r2 if r1<R and r2<R For r<R g=43π ρ Gr∴g∝ r For r>R g=GMr2∴g∝1r2 If r1 <R and r2<R then F1F2=g1g2=r1r2 If r1>R and r2>R then F1F2=g1g2=(r2r1)2

The magnitudes of the gravitational force at distances $r_{1}$ and $r_{2}$ from the centre of a uniform sphere of radius $R$ and mass $M$ are $F_{1}$ and $F_{2}$ respectively. Then