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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 451. |
Inside a uniform sphere of mass M and radius R, a cavity of radius `R//3`, is made in the sphere as shown : A. Gravitational field inside the cavity is uniformB. Gravitational field inside the cavity is non-uniformC. The escape velocity of a particle projected from point A is `sqrt((88GM)/(15R))`D. Escape velocity is defined for earth and particle system only |
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Answer» Correct Answer - A |
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| 452. |
Let V and E be the gravitational potential field. Then select the correct alternative(s) :A. The plot of E against r (distance from centre) is discontinuous for a spherical shellB. The plot of V against r is continuous for a spherical shellC. The plot of E against r is discontinuous for a solid sphereD. The plot of V against r is continuous for a solid sphere |
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Answer» Correct Answer - A::B::D |
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| 453. |
The mass of Mars is one - tenth that of the earth and its diameter is only half that of the earth . Compare the values of g on their surface . |
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Answer» Correct Answer - `2 : 5` |
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| 454. |
Mars and earth have masses in the ratio `1:11` and radii in the ratio `42:79`. Compare a. their densities, assuming them to be spheres of uniform density, b. gravitational field strengths at their surfaces: c. escape velocities from their surfaces,d. periods of their satellites near their surfaces. |
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Answer» a. `rho=M/(4/3piR^(3)` `(rho_(1))/(rho_(2))=(M_(1))/(M_(2))((R_(2))/(R_(1)))^(2)=0.605` b.` fg=-(GM)/(R^(2))` `(f_(1))/(f_(2))=(M_(1))/(M_(2))((R_(2))/(R_(1)))^(2)=1/11xx(79/42)^(2)` c. `v_(e)=sqrt((2GM)/R)` `(v_(1))/(v_(2))=sqrt((M_(1))/ M_(2) (R_(2))/(R_(1)))=sqrt(1/11xx79/42)=0.4135` d. Period near surface of planet is `T=2pisqrt(R^(3)/(GM))` `(T_(1))/(T_(2))=sqrt(((R_(1))/(R_(2)))^(3)(M_(2))/(M_(1)))=sqrt((42/79)^(3)xx11/1)=1.286` |
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| 455. |
A body weight 45 kg wt on the surface of earth. Its weight on the surface of Mars will be [Mass of Mars = (1/9) mass of earth, Radius of Mars = (1/2) Radius of earth]A. 25 kg wtB. 20 kg wtC. 30 kg wtD. 40 kg wt |
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Answer» Correct Answer - b `F_(1)=(GM_(1)m)/(R_(1)^(2)) and F_(2)=(GM_(2)m)/(R_(2)^(2))` `therefore" "(F_(2))/(F_(1))=(M_(2))/(M_(1))xx(R_(1)^(2))/(R_(2)^(2))` |
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| 456. |
A body weights 100 kg on earth . Find its weight on mars . The mass and radius of mars are 1/10 and 1/2 of the mass and radius of earth . |
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Answer» Correct Answer - 40 kg wt |
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| 457. |
Acceleration due to gravity is ‘ g ’ on the surface of the earth. The value of acceleration due to gravity at a height of 32 km above earth’s surface is (Radius of the earth = 6400 km )A. `0.9 g`B. `0.99 g`C. `0.8 g`D. `1.01 g` |
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Answer» Correct Answer - B |
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| 458. |
The total energy of a satellite moving in a circular orbit is `[-1.5xx10^(9)J]`. What is its bilding energy?A. `3xx10^(0)J`B. `1.5xx10^(9)`JC. `0.75xx10^(10)`JD. `4.5xx10^(10)`J |
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Answer» Correct Answer - B Binding energy `=-` [Total energy] `=1.5xx10^(9)J` |
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| 459. |
In a satellite if the time of revolution is `T`, then kinetic energy is proportional toA. `1/T`B. `1/(T^(2))`C. `1/(T^(3))`D. `T^(2//3)` |
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Answer» Correct Answer - B `K=1/2mv^(2)=1/2m omega^(2) R^(2)=1/2m((2pi)/T)^(2) R^(2)` `=(2pi^(2)mR^(2))/(T^(2))` `K prop 1/(T^(2))` |
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| 460. |
A metal in which even iron can float is :A. SodiumB. magnesiumC. mercuryD. manganese |
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Answer» Correct Answer - C |
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| 461. |
A rectangular wooden block has length, breadth and height of 50 cm, 25 cm and 10 cm, respectively. This wooden block is kept on ground is three different ways trun by trun .Which of the following is the correct statement about the pressure exerted by this block on the ground?A. the maximum pressure is exerted when the length and breadth form the baseB. the maximum pressure is exerted when length and height form the baseC. the maximum pressure is exerted when breadth and height form the baseD. the minimum pressure is exerted when length and height form the base |
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Answer» Correct Answer - C |
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| 462. |
Two particles are placed at some distance. If the mass of each of the two particles is doubled, keeping the distance between them unchanged, the value of gravitational force between them will beA. 1/4 timesB. 1/2 timesC. 4 timesD. 2 times |
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Answer» Correct Answer - c |
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| 463. |
A particle of mass m is moved from A to B as show in figure. Then potential energy of the the particle A. will continuously increasesB. will continuously decreasesC. will first increase and then become constantD. will first decreases and then become constant |
| Answer» Correct Answer - D | |
| 464. |
One ring of radius R and mass m and one solid sphere of same mass m and same radius R are placed with their centres on positive x-axis. We are moving from some finite distance on negative x-axis towards positive x-axis plane of the ring is perpendicular to x-axis. How will the net gravitational field vary with distance moved on x-axis We move only up to surface of solid sphere. O is the origin. A. B. C. D. |
| Answer» Correct Answer - C | |
| 465. |
A particle of mass m is moving along the line y-b with constant acceleration a. The areal velocity of the position vector of the particle at time t is `(u=0)`A. constantB. `(abt)/(2)`C. `(abt)/(2m)`D. `(a^(2)bt)/(2m)` |
| Answer» Correct Answer - B | |
| 466. |
A mass is taken from surface to a height h. The change in potential energy in this process is equal to the change in potential energy if it is now taken from that point to infinity. What is the value of h?A. `h=R`B. `h=2R`C. `h=(3R)/(2)`D. `h=4R` |
| Answer» Correct Answer - A | |
| 467. |
If radius of a solid sohere is decreases to half, keeping density of sphere unchanged, the slope of E-r graph inside the sphere willA. remain unchangedB. become two timesC. become four timesD. remain `(1)/(8)` th |
| Answer» Correct Answer - A | |
| 468. |
Four balls,A,B,C,D displace 10 mL ,24 mL,15 mL, and 12 mL of a liquid respectively ,when immersed completely.The ball which will undergo the maximum apparent loss in weight will be :A. AB. BC. CD. D |
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Answer» Correct Answer - B |
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| 469. |
At what distance from the center of the earth will a 1 kg object have a weight of `1 N` ? If released from rest at this distance, What will its initial acceleration be ? |
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Answer» Correct Answer - `2.023 xx 10^(7)m` |
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| 470. |
Suppose we invent a unit of mass which we shall call the caendish (C). One cavendish of mass is defined such that `G = 1.0000(AU)^(3)//(yr^(2)C)`. Our unit of length is the astronomical unit `(AU)`, the earth-sun distance`-1AU = 1.496 xx 10^(11) m`- and our unit of time is the year `(yr)`. (a) Datermine the conversion factor between C and kg. (b) Find the mass of the sun in C. |
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Answer» Correct Answer - (a) `1.984 xx 10^(-29) C//kg`; (b) `39.5 C` |
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| 471. |
In figure-6.105, particle A has a mass of `1.4` and particle B has a mass of `3.1 kg`. What is the gravitational field at point P ? |
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Answer» Correct Answer - `vectorg = (2.2 xx 10^(-11) N//kg)hati - (5.5 xx 10^(-11) N//kg)hatj` |
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| 472. |
A pendulum beats seconds on the surface of the Earth. Calculate as to how much it loses or gains per day if it is taken to, (a) a mass 8 km below, (b) a point 8 km above, the surface. (Radius of the Earth `= 6.4 xx 10^(6)m`) |
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Answer» Correct Answer - (a) `54` sec; (b) `107.9` sec |
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| 473. |
A body is imparted a velocity v from the surface of the earth. If `v_(0)` is orbital velocity and `v_(e)` be the escape velocity then for : `v = v_(0)` the body follows a circular track around the earth. (B). `v gt v_(0)` but `lt ve`, the body follows elliptical path around the earth. (C). `v lt v_(0)`, the body follows elliptical path and return to surface of earth. (D). `v gt v_(e)`, the body follows hyperbolic path and escape the gravitational pull of the earth.A. A, BB. B, CC. A, B, CD. A, B, C, D |
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Answer» Correct Answer - D |
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| 474. |
Suppose universal gravitational constant starts to decrease, thenA. Length of the year will increaseB. Earth will follow a spiral path of decreasing radiusC. Kinetic energy of earth will decreaseD. All of the above |
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Answer» Correct Answer - A::C |
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| 475. |
A body is imparted a velocity v from the surface of the earth. If `v_(0)` is orbital velocity and `v_(e)` be the escape velocity then for :A. `v = v_(0)` the body follows a circular track around the earth.B. `v gt v_(0)`, but `lt v_(e)`, the body follows elliptical path around the earthC. `v lt v_(0)`, the body follows elliptical path and returns to surface of earthD. `v gt v_(e)`, the body follows hyperbolic path and escapes the gravitational pull of the earth |
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Answer» Correct Answer - A::B::C::D |
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| 476. |
State any four applications of a communication satellite. |
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Answer» Applications of communication satellite : 1. For the transmission of television and radio wave signals over large areas of Earth’s surface. 2. For broadcasting telecommunication. 3. For military purposes. 4. For navigation surveillance. |
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| 477. |
A plantet is moving round the sun in an elliptical orbit as shows. As the planet moves from `a` to `B` A. its kinetic enargy will decreaseB. its potential energy will remain unchangedC. its angular momentum about centre of sun will remain unchangedD. its speed is minimum at `A` |
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Answer» Correct Answer - C::D At maximum distance (at `A` ) kinetic energy is minimum. But angular momentum about centre of sun always remains constant. |
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| 478. |
A particle of mass m was transferred from the centre of the base of a uniform hemisphere of mass M and radius R into infinity. What work was performed in the process by the gravitational force exerted on the particle by the hemisphere?A. `(GMm)/(R)`B. `-(1)/(2)(GMm)/(R)`C. `-(3)/(2)(GMm)/(R)`D. `-(3)/(4)(GMm)/(R)` |
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Answer» Correct Answer - C P.E. of the system is equal to `U_(i)=-(3GMm)/(2R)` work done `implies-DeltaUimplies-[U_(f)-U_(i)]impliesU_(i)implies-(3GMm)/(2R)` |
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| 479. |
At what height the acceleration due to gravity decreasing by 51 % of its value on the surface of th earth ? |
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Answer» As, `g_(h)=g((R)/(R+h))^(2) and g_(h)=g-51%` of `g=g-(51)/(100)g` `:. g_(h)=(49)/(100)g` `:. (49)/(100)g=g((R)/(R+h))^(2)` `:.(7)/(10)=(R)/(R+h)` `:. 7R+7h=10R` `:. 7h=3RrArrh=(3R)/(7)`. |
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| 480. |
The length of a seconds pendulum on the surface of the Earth is 100 cm. Find the length of the seconds pendulum on the surface of the moon. `("Take",g_(M) = (1)/(6)g_(E))`A. 1.66 mB. 16.6 cmC. 33.2 cmD. 3.32 m |
| Answer» Correct Answer - B | |
| 481. |
If `S_1` is surface satellite and `S_2` is geostationary satellite, with time periods `T_1` and `T_2`, orbital velocities `V_1` and `V_2`,A. `T_(1)gtT_(2),V_(1)gtV_(2)`B. `T_(1)gtT_(2),V_(1)ltV_(2)`C. `T_(1)ltT_(2),V_(1)ltV_(2)`D. `T_(1)ltT_(2),V_(1)gtV_(2)` |
| Answer» Correct Answer - D | |
| 482. |
If a satellite moves tangent to the circular path, thenA. `v_(h) lt v_(c)`B. `v_(c)=v_(h)`C. `v_(c) lt v_(h) lt v_(e)`D. `v_(h) gt v_(e)` |
| Answer» Correct Answer - d | |
| 483. |
A geostationary satelliteA. revolves about the polar axisB. has a time period less than that of the near earth satelliteC. moves faster than a near earth satelliteD. is stationary in the space |
| Answer» Correct Answer - a | |
| 484. |
If the angular velocity of a planet about its own axis is halved, the distance of geostationary satellite of this planet from the centre of the centre of the planet will becomeA. `(2)^(1//2)` timesB. `(2)^(3//2)`timesC. `(2)^(2//3)` timesD. 4 times |
| Answer» Correct Answer - C | |
| 485. |
A geostationary satellite is going round the Earth in an orbit. Then, which of the following statements are true? (A) It is like a freely falling body. (B) It posseses acceleration throughtout its journey. (C) Its is moving with constant speed. (D) It is moving with constant velocityA. ABCB. BCDC. CDAD. DAB |
| Answer» Correct Answer - A | |
| 486. |
Astronauts in a stable orbit around the earth are said to be in a weightless condition. The reason for this is thatA. the capsule and its contents are falling freely at the same rateB. there is no gravitational force action on themC. the gravitational force of ht earth balances that of the sunD. there is no atmosphere at the height at which they are orbiting |
| Answer» Correct Answer - a | |
| 487. |
An astronaut experiences weightlessness in a space satellite It is because .A. the gravitational force is small at that location in space.B. the gravitational force is large at that location in space.C. the astronaut experiences no gravity.D. the gravitational force is infinitely large at that location in space. |
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Answer» Correct Answer - C An astronaut experiences weight lessesness in a space satellite. It is because the astornaut experieneces no gravity. |
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| 488. |
A satellite is moveing in a circular orbit around the earth. The total energy of the satellite is `E=-2xx10^(5) J`. The amount of energy to be imparted to the satellite to transfer it to be orbit where its potential energy is `U=-2xx10^(5)J` is equal to ................ |
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Answer» Correct Answer - `1xx10^(5)J` `E_(1)=(U_(1))/2impliesE_(2)=(U_(2))/2=-xx10^(5)J` `E_(1)=-2xx10^(5)J` So `DeltaE=E_(2)-E_(1)=1xx10^(5)J` |
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| 489. |
If the kinetic energy of a satellite is `2xx10^(4)J`, then its potential energy will beA. `-2xx10^(-4)J`B. `4xx10^(4)J`C. `-4xx10^(4)J`D. `-10^(4)J` |
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Answer» Correct Answer - c `P.E.=-2KE` `=2xx210^(4)=4xx10^(4)J.` |
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| 490. |
A satellite of mass m is orbiting the earth at a height h from its surface. If M is the mass of the earth and R its radius, the kinetic energy of the stellite will beA. `-(GmM)/((R+h)^(2))`B. `(GmM)/(2(R+h)^(2))`C. `(GmM)/((R+h))`D. `(GmM)/(2(R+h))` |
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Answer» Correct Answer - d `K.E.=(1)/(2)mv_(c)^(2)` `=(1)/(2)m(GM)/(r)=(1)/(2)(GMm)/((R+h))` |
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| 491. |
The maximum possible velocity of a satellite orbiting round the earth in a stable orbit isA. `sqrt(2R_(e) g)`B. `sqrt(R_(e) g)`C. `sqrt((R_(e)g)/2)`D. Infinite |
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Answer» Correct Answer - B |
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| 492. |
The orbital speed for an earth satellite near the surface of the earth is `7km//sec`. If the radius of the orbit is `4` times the radius of the earth, the orbital speed would beA. `3.5 km//s`B. `7 km//s`C. `7sqrt2 km//s`D. `14 km//s` |
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Answer» Correct Answer - A `V_(0)=sqrt((GM)/r)rArrV_(0)prop1/(sqrt(r))` |
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| 493. |
In above equation No. 304, the potential energy of the satellite isA. `-(GmM)/((R+h)^(2))`B. `-(GmM)/(2(R+h)^(2))`C. `-(GmM)/((R+h))`D. `-(GmM)/(2(R+h))` |
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Answer» Correct Answer - c `"Potential energy "=-(GmM)/(r)=-(GmM)/((R+h))`. |
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| 494. |
The binding energy of a system of earth and its satellite orbiting round the earth in a circular orbit is E. If m of that satellite, its linear speed in that orbit isA. `2E//m`B. `E//m`C. `sqrt(2E//m)`D. `sqrt(E//m)` |
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Answer» Correct Answer - c `E=(GMm)/(2r)=(1)/(2)mv_(e)^(2)` `v_(c)^(2)=(2E)/(m)` `therefore" "v_(c)=sqrt((2E)/(m)).` |
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| 495. |
A satellite is orbiting the earth in a circular orbit of radius `r`. ItsA. A and BB. A and CC. A, C and DD. all of the above |
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Answer» Correct Answer - c `"K.E. " prop (1)/(r), L=Iomega="mrV = mr"sqrt((GM)/(r))=msqrt(GMr)` `therefore" "L prop sqrtr, P=mV=msqrt((GM)/(r)) therefore P prop (1)/(sqrtr),` `therefore T prop r^(3//2)" "therefore (f)/(n) prop (1)/(r^(3//2))` |
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| 496. |
Does the escape speed of a body from the earth depend on (a) the mass of the body. (b) the location from where it is projected. © the direction of projection, (d) the height of the location from where the body is launched? |
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Answer» The escape speed `v_(es)=sqrt((2GM)/R)=sqrt(gR)`. Hence, The escape speed of a body from the Earth does not depend on the mass of the body.(b) The escape speed does not depend on the location from where a body is projected.(c) The escape speed does not depend on the direction of projection of a body.(d) The escape speed of a body depends upon the height of the location from where the body is projected, because the escape velocity depends upon the gravitational potential at the point from which it is projected and this potential depends upon height also. |
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| 497. |
On which factors does the escape speed of a body from the surface of Earth depend? |
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Answer» The escape speed depends only on the mass and radius of the planet. [Note: Escape velocity does not depend upon the mass of the body] |
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| 498. |
Gas escaps from the surface of a planet because it acquires an escape velocity. The escape velocity will depend on which of the following factors : I. Mass of the planet II. Mass pf the particle escaping III. Temperature of the planet IV. Radius of the planet Select the correct answer from the codes given below.A. I and IIB. II and IVC. I and IVD. I, II and IV |
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Answer» Correct Answer - C `v_(e)=sqrt((2GM)/(R))` i.e., escape velocity depends upon the mass and radius of the planet. |
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| 499. |
Gas escapes from the surface of a planet because it acquires an escape velocity. The escape velocity will depend on which of the following factors: (1) Mass of the planet (2) Radius of the planet (3) Mass of the particle escaping (4) Temperature of the planetA. I and IIB. II and IVC. I and IVD. I, III and IV |
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Answer» Correct Answer - C |
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| 500. |
Two satellite are revolving round the earth at different heights. The ratio of their orbital speeds is `2:1`. If one of them is at a height of the other satellite is (in `km`)A. `19600`B. `24600`C. `29600`D. `14600` |
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Answer» Correct Answer - A `V_(0)=sqrt((GM)/(R+h))rArr V_(0)prop1/(sqrt(R+h))` |
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