Physics NCERT Exemplar Solutions Class 11th Chapter Eight

Answer-c

Explanation-The gravitational force between sun and earth follows inverse square law. Due to relative motion between earth and mercury, the orbit of mercury observed from the earth will not be approximately circular since the major gravitational force on mercury is due to the sun.

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Answer-d

Explanation- We treated that the mass of earth is at centre . in this case a=g=0 at centre but if earth is not uniform then value of g is different at different point.

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Explanation- Gravitational force at h height F = $\frac{GMmh}{{{(r}^2+h^2)}^{3/2}}$

When mass is displaced upto distance 2h then

F'= $\frac{GMm2h}{{{[r}^2+{\left(2h\right)]}^2]}^{\frac{3}{2}}}$

= $\frac{2GMmh}{{\left(r^2+4h^2\right)}^{\frac{3}{2}}}$

When h = r then F= $\frac{GMmh}{[{r^2+{\left(r\right)}^2]}^{3/2}}$

So F = $\frac{GMm}{2\sqrt[]{2r^2}}$

F'= $\frac{2GMmr}{{\left(r^2+4r^2\right)}^{\frac{3}{2}}}=\frac{2GMm}{5\sqrt[]{5r^2}}$

$\frac{F^{\text{'}}}{F}=\frac{4\sqrt[]{2}}{5\sqrt[]{5}}$

F' = $\frac{4\sqrt[]{2}}{5\sqrt[]{5}}F$

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Explanation-potential energy of the objects at the surface of the earth is =- $\frac{GMm}{R}$

PE of the object at a height equal to radius of earth = $\frac{GMm}{2R}$

Gain in potential energy = $\frac{GMm}{2R}$ - (- $\frac{GMm}{R}$ )= $\frac{GMm}{2R}$

= $\frac{g{R}^{2}m}{2R}=\frac{1}{2}mgR$ (GM=gR²)

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Explanation-The trajectory of a particle under gravitational force of the earth will be in conic section with the centre of the earth as a focus. Only c meets this requirements

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Explanation- Orbital speed of the satellite v_o= $\sqrt[]{\frac{GM}{R}}$

KE of the satellite of mass m, E_k = 1/2mv_o²= Gmm/2R              

So kinetic energy is inversely proportional to distance.

b)potential energy of a satellite E_p=-GMm/R

so it is also inversely proportional to R

c)total energy of the satellite E=E_k+E_p = $\frac{GMm}{2R}-\frac{GMm}{R}$ = - $\frac{GMm}{2R}$

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Explanation- Let M be the mass and R be the radius of sphere . an object of mass m be placed at the mid point P of the line joining their centres

Force F₁=F₂=GMm/ (5R)²

If we displace it through x distance

New force towards sphere A, F₁'= GMm/ (5R-x)²

Sphere B F₂' = GMm/ (5R+x)²

As F₁'>F₂' therefore a resultant force (F₁'-F₂') acts on the objects towards sphere A therefore objects start to move towards A hence equilibrium is unstable.

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Explanation-Every day the earth advances in the orbit by approximately 1⁰. Then it will have to rotate by 361⁰ to have the sun at zenith point again. So 361⁰ corresponds to 24h

So 1^o corresponds to 24/361= 0.066h=3.99 min =4min

Hence distant stars would rise 4 min early every successive day.

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Explanation- Angle between the equatorial plane and orbital plane of a polar satellite is 90⁰ and angle between equatorial plane and orbital plane of a geostationary satellite is 0⁰.

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Explanation- Phelion is the location of the earth where it is the greatest distance from the sun and perihelion is the location of the earth where it is the nearest to the sun

The areal velocity (1/2 rv) of the earth around the sun is constant . so speed of earth is more at perihelion.