A small block of superdennse material has a mass of `3xx10^24` kg. It is situated at a height h (much smaller than the earth's radius) from where it falls on the earth's surface. Find its speed when its height from the earth's surface has reduced to `h/2`. The mass of the earth is `6xx10^24kg`

Answer

B, C

Explanation

Given hltltltR
G mass `=6dxx10^24kg`
`mgb=3xx10^24` kg
let `V_erarr` velocity of earth
`V_brarr `velocity of the block
The two blocks are attached by gravittionl force of attrction. The gravitation potential energy stored will be the K.E. of two blocks
GM_em_b 1/(R+(h/2))=1/(R+h)`
`=(1/2)m_3xxv_2^2+(1/2)M_bxxv_b^2`
Again as the inteN/Al force acts
`M_eV_e=M_bV_b`

`rarr V_e=(M_bV_b)/M_e` ...........iii ltbr. putting equation i
`Gm_exxm_b[2/(2R+h)-1/(R+h)]`
`=(1/2)xxM_exx(M_b^2V_b^2)/M_e^2+(1/2)xxM_bxxV_b^2`
`=(1/2)xxM_xxV_b^2 M_b/M_e+1/2xxM_bxxv_b^2`
`rarr GM_e (2R+2h-2R-h)/((2R+h)(R+h))`
`=(1/2)xxv_b^2xx((3x10^24)/(6x10^24)+1)`
`rarr [(GMxxh)/(2R^2)]=(1/2)xxV_b^2xx(3/2)`
`rarr gh=V_b^2xx(3/2)`
`V_b=(2gh)/3`