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

A particle is fired vertically upward with a speed of `15 kms^-1`. With what speed will it move it intersteller space. Assume only earth's gravitational field.

Text Solution

Verified by Experts

The correct Answer is:
A
Initial velocity of the particle `=15 km/s`
let its speed be V at intesteller space
`=:.(1/2)m[15xx10^3-V^2]=int_R^oo (GMm)/x^2dx`
rarr (1/2)m[(15xx10^3)^2-V^2]=GMm[(-1)/x]`
`rarr (1/2)m[(225xx10^5)-v^2]=(GMm)/R`
`rarr 225xx10^5-v^2=(2xx6.67xx6xx10^24)/(6400xx10^3)`
`rarr v^2=225xx10^6-40.02/32xx10^8`
`=2.25xx10^8-1.2xx10^8`
`=10^98(1.05)`
`or v=1.01xx10^4m/s`
`=10 km/s`
Promotional Banner

Similar Questions

Explore conceptually related problems

A particle is projected vertically upwards with a speed of 16ms^-1 . After some time, when it again passes through the point of projection, its speed is found to be 8ms^-1 . It is known that the work done by air resistance is same during upward and downward motion. Then the maximum height attained by the particle is (take g=10ms^-2 )

A particle is thrown in vertically upward direction, the correct graph of speed (v) to time (1) is ......

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?

From a tower of height H , a particle is thrown vertically upwards with a speed u . The time taken by the particle , to hit the ground , is n times that taken by it to reach the highest point of its path. The relative between H, u and n is :

A rocket is fired vertically with a speed of 5 km s^(-1) from the earth’s surface. How far from the earth does the rocket go before returning to the earth ? Mass of the earth = 6.0 × 10^(24) kg, mean radius of the earth = 6.4 xx 10^(6) m , G = 6.67 xx 10^(-11) " N "m^(2) kg^(-2) .

A particle is thrown vertically upward with a speed u from the top of a tower of height h from ground level, If after first impact with ground it just reaches to height h from ground the coeffecient of restitution for the collision 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 man is moving due east with a speed 1 km/hr and rain is falling vertically with a speed sqrt(3) km/hr. At what angle from vertical the man has to hold his umbrella to keep the rain away. Also find the speed of rain drops w.r.t. man.

Assume that a tunnel is dug across the earth (radius=R) passing through its centre. Find the time a particle takes to reach centre of earth if it is projected into the tunnel from surface of earth with speed needed for it to escape the gravitational field to earth.