Home
Class 11
PHYSICS
A particle is fired vertically upward fo...

A particle is fired vertically upward fom earth's surface and it goes up to a maximum height of 6400 km. find the initial speed of particle.

Text Solution

Verified by Experts

The correct Answer is:
A
The particle attain maximum height =6400 km
On earth's surface its P.E. and K.E.
`E_e=1/2MV^2+((-gmM)/r)`…….. 1
In space its P.E. and K.E.
`E_3=((-GMm)/(R+h))+0`
`E_3=((-GMm)/(2R))`……….2 `(:.g=R)`
Equation 1 and 2
`=-(GMm)/R+1/2mv^2=-(GMm)/(2R)`
or `(1/2)mv^2=GMm(-1/(2R)+1/R)`
`v^2=(GM)/R`
`=(6.67xx10^-11xx6xx10^24)/(6400xx10^3)`
`(40.02+10^13)/(6.4xx10^6)`
`=6.2xx10^7=0.62x10^8`
or `v=sqrt(0.62xx10^8)`
`=0.79xx10^4m/s`
`=79km/s`
Promotional Banner

Similar Questions

Explore conceptually related problems

A particle is projected vertically upwards and it reaches the maximum height H in time T seconds. The height of the particle at any time t will be-

Show that if a body is projected vertically upward from the surface of the earth so as to reach a height nR above the surface (i) the increase in its potential energy is ((n)/(n + 1)) mgR , (ii) the velocity with which it must be projected is sqrt((2ngR)/(n + 1)) , where r is the radius of the earth and m the mass of body.

There is crater of depth R//100 on the surface of the moon (raduis R ). A projectile is fired vertically upwards from the crater with a velocity, which is equal to the escape velocity v from the surface of the moon. The maximum height attained by the projectile, is :

A projectile is fired vertically upwards from the surface of the earth with a velocity Kv_(e) , where v_(e) is the escape velocity and Klt1 .If R is the radius of the earth, the maximum height to which it will rise measured from the centre of the earth will be (neglect air resistance)

A rocket is fired ‘vertically’ from the surface of mars with a speed of 2 km s^(–1) . If 20% of its initial energy is lost due to martian atmospheric resistance, how far will the rocket go from the surface of mars before returning to it ? Mass of mars = 6.4 xx 10^(23) kg, radius of mars = 3395 km, G = 6.67 xx 10^(-11) N m^(2) Kg^(-2) .

A particle is projected vertically upwards the surface of the earth (radius R_(e)) with a speed equal to one fourth of escape velocity what is the maximum height attained by it from the surface of the earth?

A particle is projected vertically upwards from the earth. It crosses the same point at t=2 sec and t=8 sec. Find out [g=10 ms^(-2)] initial velocity of particle

A ball is projected vertically up with a speed of 50 m/s. Find the maximum height , the time to reach the maximum height, and the speed at the maximum height (g=10 m//s^(2)) (AS_(1))

A particle is projected vertically upwards from ground with velocity 10 m // s. Find the time taken by it to reach at the highest point ?