138602
A planet revolves around the sun in an elliptical orbit. The linear speed of the planet will be maximum at
1 $\mathrm{D}$
2 $\mathrm{B}$
3 $\mathrm{A}$
4 $\mathrm{C}$
Explanation:
C Suppose that, According to Kepler's second law, when a planet is closer to the sun, it travels faster. $\because$ Angular momentum $=$ constant $\mathrm{v} \propto \frac{1}{\mathrm{r}}$ $\mathrm{mvr}=\text { constant }$ Linear speed of a planet is maximum when its distance from the sun is least. So, A is the least distance from sun. Hence the linear speed is maximum.
UPCPMT 2007
Gravitation
138603
The period of a planet around sun is 27 times that of earth. The ratio of radius of planet's orbit of the radius of earth's orbit is
1 4
2 9
3 64
4 27
Explanation:
B Let, $\mathrm{T}_{\mathrm{p}}=$ Period of Planet $\mathrm{T}_{\mathrm{e}}=$ Period of Earth $\mathrm{R}_{\mathrm{p}}=$ Radius of Planet $\mathrm{R}_{\mathrm{e}}=$ Radius of Earth Given, $\mathrm{T}_{\mathrm{P}}=27 \mathrm{~T}_{\mathrm{e}}$ Using Kepler's third law of periods $\mathrm{T}^{2} \propto \mathrm{R}^{3}$ $\therefore \quad \mathrm{T}_{\mathrm{p}}^{2} \propto \mathrm{R}_{\mathrm{p}}^{3}$ $\mathrm{~T}_{\mathrm{e}}^{2} \propto \mathrm{R}_{\mathrm{e}}^{3}$ Dividing equation (i) by equation (ii) we get - $\left(\frac{T_{p}}{T_{e}}\right)^{2}=\left(\frac{R_{p}}{R_{e}}\right)^{3}$ $\left(\frac{27 T_{e}}{T_{e}}\right)^{2}=\left(\frac{R_{p}}{R_{e}}\right)^{3}$ $\left(\frac{R_{p}}{R_{e}}\right)^{3}=(27)^{2}=3^{6}$ $\frac{R_{p}}{R_{e}}=(3)^{2}$ $R_{p}=9 R_{e}$
Manipal UGET-2010
Gravitation
138604
A planet is revolving around the sun in elliptical path as shown in the figure. Which of the following is correct statement?
1 The time taken in travelling DAB is less than that for BCD.
2 The time taken in travelling DAB is greater than that for BCD.
3 The time taken in travelling CDA is less than that for $\mathrm{ABC}$.
4 The time taken in travelling CDA is greater than that for $\mathrm{ABC}$.
Explanation:
A When the planet is near to the sun its speed is more. During path $\mathrm{DAB}$ planet is nearer to the sun as comparison with path BCD. So time taken in travelling $\mathrm{DAB}$ is less than that for $\mathrm{BCD}$ because velocity of planet will be more in region DAB.
TS- EAMCET-09.09.2020
Gravitation
138605
Assertion: The length of the day is slowly increasing. Reason: The dominant effect causing a slowdown in the rotation of the earth is the gravitational pull of other planets in the solar system.
1 If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
2 If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
3 If the Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
5 If the Assertion is incorrect but the Reason is correct.
Explanation:
C Due to viscous force between the earth and the atmosphere around length of the day is slowly increasing. Angular speed of the earth is given by $\omega=\frac{2 \pi}{\mathrm{T}}$ Length of day $(T)$ depends upon angular speed $(\omega)$ of the earth about its own axis. Also Kepler's second law of motion which is also law of conservation of angular momentum holds true for sun-earth system. Earth rotation is not slowing down. So, Assertion is correct but Reason is incorrect.
138602
A planet revolves around the sun in an elliptical orbit. The linear speed of the planet will be maximum at
1 $\mathrm{D}$
2 $\mathrm{B}$
3 $\mathrm{A}$
4 $\mathrm{C}$
Explanation:
C Suppose that, According to Kepler's second law, when a planet is closer to the sun, it travels faster. $\because$ Angular momentum $=$ constant $\mathrm{v} \propto \frac{1}{\mathrm{r}}$ $\mathrm{mvr}=\text { constant }$ Linear speed of a planet is maximum when its distance from the sun is least. So, A is the least distance from sun. Hence the linear speed is maximum.
UPCPMT 2007
Gravitation
138603
The period of a planet around sun is 27 times that of earth. The ratio of radius of planet's orbit of the radius of earth's orbit is
1 4
2 9
3 64
4 27
Explanation:
B Let, $\mathrm{T}_{\mathrm{p}}=$ Period of Planet $\mathrm{T}_{\mathrm{e}}=$ Period of Earth $\mathrm{R}_{\mathrm{p}}=$ Radius of Planet $\mathrm{R}_{\mathrm{e}}=$ Radius of Earth Given, $\mathrm{T}_{\mathrm{P}}=27 \mathrm{~T}_{\mathrm{e}}$ Using Kepler's third law of periods $\mathrm{T}^{2} \propto \mathrm{R}^{3}$ $\therefore \quad \mathrm{T}_{\mathrm{p}}^{2} \propto \mathrm{R}_{\mathrm{p}}^{3}$ $\mathrm{~T}_{\mathrm{e}}^{2} \propto \mathrm{R}_{\mathrm{e}}^{3}$ Dividing equation (i) by equation (ii) we get - $\left(\frac{T_{p}}{T_{e}}\right)^{2}=\left(\frac{R_{p}}{R_{e}}\right)^{3}$ $\left(\frac{27 T_{e}}{T_{e}}\right)^{2}=\left(\frac{R_{p}}{R_{e}}\right)^{3}$ $\left(\frac{R_{p}}{R_{e}}\right)^{3}=(27)^{2}=3^{6}$ $\frac{R_{p}}{R_{e}}=(3)^{2}$ $R_{p}=9 R_{e}$
Manipal UGET-2010
Gravitation
138604
A planet is revolving around the sun in elliptical path as shown in the figure. Which of the following is correct statement?
1 The time taken in travelling DAB is less than that for BCD.
2 The time taken in travelling DAB is greater than that for BCD.
3 The time taken in travelling CDA is less than that for $\mathrm{ABC}$.
4 The time taken in travelling CDA is greater than that for $\mathrm{ABC}$.
Explanation:
A When the planet is near to the sun its speed is more. During path $\mathrm{DAB}$ planet is nearer to the sun as comparison with path BCD. So time taken in travelling $\mathrm{DAB}$ is less than that for $\mathrm{BCD}$ because velocity of planet will be more in region DAB.
TS- EAMCET-09.09.2020
Gravitation
138605
Assertion: The length of the day is slowly increasing. Reason: The dominant effect causing a slowdown in the rotation of the earth is the gravitational pull of other planets in the solar system.
1 If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
2 If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
3 If the Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
5 If the Assertion is incorrect but the Reason is correct.
Explanation:
C Due to viscous force between the earth and the atmosphere around length of the day is slowly increasing. Angular speed of the earth is given by $\omega=\frac{2 \pi}{\mathrm{T}}$ Length of day $(T)$ depends upon angular speed $(\omega)$ of the earth about its own axis. Also Kepler's second law of motion which is also law of conservation of angular momentum holds true for sun-earth system. Earth rotation is not slowing down. So, Assertion is correct but Reason is incorrect.
138602
A planet revolves around the sun in an elliptical orbit. The linear speed of the planet will be maximum at
1 $\mathrm{D}$
2 $\mathrm{B}$
3 $\mathrm{A}$
4 $\mathrm{C}$
Explanation:
C Suppose that, According to Kepler's second law, when a planet is closer to the sun, it travels faster. $\because$ Angular momentum $=$ constant $\mathrm{v} \propto \frac{1}{\mathrm{r}}$ $\mathrm{mvr}=\text { constant }$ Linear speed of a planet is maximum when its distance from the sun is least. So, A is the least distance from sun. Hence the linear speed is maximum.
UPCPMT 2007
Gravitation
138603
The period of a planet around sun is 27 times that of earth. The ratio of radius of planet's orbit of the radius of earth's orbit is
1 4
2 9
3 64
4 27
Explanation:
B Let, $\mathrm{T}_{\mathrm{p}}=$ Period of Planet $\mathrm{T}_{\mathrm{e}}=$ Period of Earth $\mathrm{R}_{\mathrm{p}}=$ Radius of Planet $\mathrm{R}_{\mathrm{e}}=$ Radius of Earth Given, $\mathrm{T}_{\mathrm{P}}=27 \mathrm{~T}_{\mathrm{e}}$ Using Kepler's third law of periods $\mathrm{T}^{2} \propto \mathrm{R}^{3}$ $\therefore \quad \mathrm{T}_{\mathrm{p}}^{2} \propto \mathrm{R}_{\mathrm{p}}^{3}$ $\mathrm{~T}_{\mathrm{e}}^{2} \propto \mathrm{R}_{\mathrm{e}}^{3}$ Dividing equation (i) by equation (ii) we get - $\left(\frac{T_{p}}{T_{e}}\right)^{2}=\left(\frac{R_{p}}{R_{e}}\right)^{3}$ $\left(\frac{27 T_{e}}{T_{e}}\right)^{2}=\left(\frac{R_{p}}{R_{e}}\right)^{3}$ $\left(\frac{R_{p}}{R_{e}}\right)^{3}=(27)^{2}=3^{6}$ $\frac{R_{p}}{R_{e}}=(3)^{2}$ $R_{p}=9 R_{e}$
Manipal UGET-2010
Gravitation
138604
A planet is revolving around the sun in elliptical path as shown in the figure. Which of the following is correct statement?
1 The time taken in travelling DAB is less than that for BCD.
2 The time taken in travelling DAB is greater than that for BCD.
3 The time taken in travelling CDA is less than that for $\mathrm{ABC}$.
4 The time taken in travelling CDA is greater than that for $\mathrm{ABC}$.
Explanation:
A When the planet is near to the sun its speed is more. During path $\mathrm{DAB}$ planet is nearer to the sun as comparison with path BCD. So time taken in travelling $\mathrm{DAB}$ is less than that for $\mathrm{BCD}$ because velocity of planet will be more in region DAB.
TS- EAMCET-09.09.2020
Gravitation
138605
Assertion: The length of the day is slowly increasing. Reason: The dominant effect causing a slowdown in the rotation of the earth is the gravitational pull of other planets in the solar system.
1 If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
2 If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
3 If the Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
5 If the Assertion is incorrect but the Reason is correct.
Explanation:
C Due to viscous force between the earth and the atmosphere around length of the day is slowly increasing. Angular speed of the earth is given by $\omega=\frac{2 \pi}{\mathrm{T}}$ Length of day $(T)$ depends upon angular speed $(\omega)$ of the earth about its own axis. Also Kepler's second law of motion which is also law of conservation of angular momentum holds true for sun-earth system. Earth rotation is not slowing down. So, Assertion is correct but Reason is incorrect.
138602
A planet revolves around the sun in an elliptical orbit. The linear speed of the planet will be maximum at
1 $\mathrm{D}$
2 $\mathrm{B}$
3 $\mathrm{A}$
4 $\mathrm{C}$
Explanation:
C Suppose that, According to Kepler's second law, when a planet is closer to the sun, it travels faster. $\because$ Angular momentum $=$ constant $\mathrm{v} \propto \frac{1}{\mathrm{r}}$ $\mathrm{mvr}=\text { constant }$ Linear speed of a planet is maximum when its distance from the sun is least. So, A is the least distance from sun. Hence the linear speed is maximum.
UPCPMT 2007
Gravitation
138603
The period of a planet around sun is 27 times that of earth. The ratio of radius of planet's orbit of the radius of earth's orbit is
1 4
2 9
3 64
4 27
Explanation:
B Let, $\mathrm{T}_{\mathrm{p}}=$ Period of Planet $\mathrm{T}_{\mathrm{e}}=$ Period of Earth $\mathrm{R}_{\mathrm{p}}=$ Radius of Planet $\mathrm{R}_{\mathrm{e}}=$ Radius of Earth Given, $\mathrm{T}_{\mathrm{P}}=27 \mathrm{~T}_{\mathrm{e}}$ Using Kepler's third law of periods $\mathrm{T}^{2} \propto \mathrm{R}^{3}$ $\therefore \quad \mathrm{T}_{\mathrm{p}}^{2} \propto \mathrm{R}_{\mathrm{p}}^{3}$ $\mathrm{~T}_{\mathrm{e}}^{2} \propto \mathrm{R}_{\mathrm{e}}^{3}$ Dividing equation (i) by equation (ii) we get - $\left(\frac{T_{p}}{T_{e}}\right)^{2}=\left(\frac{R_{p}}{R_{e}}\right)^{3}$ $\left(\frac{27 T_{e}}{T_{e}}\right)^{2}=\left(\frac{R_{p}}{R_{e}}\right)^{3}$ $\left(\frac{R_{p}}{R_{e}}\right)^{3}=(27)^{2}=3^{6}$ $\frac{R_{p}}{R_{e}}=(3)^{2}$ $R_{p}=9 R_{e}$
Manipal UGET-2010
Gravitation
138604
A planet is revolving around the sun in elliptical path as shown in the figure. Which of the following is correct statement?
1 The time taken in travelling DAB is less than that for BCD.
2 The time taken in travelling DAB is greater than that for BCD.
3 The time taken in travelling CDA is less than that for $\mathrm{ABC}$.
4 The time taken in travelling CDA is greater than that for $\mathrm{ABC}$.
Explanation:
A When the planet is near to the sun its speed is more. During path $\mathrm{DAB}$ planet is nearer to the sun as comparison with path BCD. So time taken in travelling $\mathrm{DAB}$ is less than that for $\mathrm{BCD}$ because velocity of planet will be more in region DAB.
TS- EAMCET-09.09.2020
Gravitation
138605
Assertion: The length of the day is slowly increasing. Reason: The dominant effect causing a slowdown in the rotation of the earth is the gravitational pull of other planets in the solar system.
1 If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
2 If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
3 If the Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
5 If the Assertion is incorrect but the Reason is correct.
Explanation:
C Due to viscous force between the earth and the atmosphere around length of the day is slowly increasing. Angular speed of the earth is given by $\omega=\frac{2 \pi}{\mathrm{T}}$ Length of day $(T)$ depends upon angular speed $(\omega)$ of the earth about its own axis. Also Kepler's second law of motion which is also law of conservation of angular momentum holds true for sun-earth system. Earth rotation is not slowing down. So, Assertion is correct but Reason is incorrect.
