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Distance between the centres of two stars is 10a. Themasses of these stars are M and 16M and their radii a and 2a respectively. A body of mass m is fired straight from the surface of the larger star towards the smaller star. The minimum initial speed for the body to reach the surface of smaller star is |
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Answer» `2/3sqrt((Gm)/a)`  i.e., once the body reaches P, the gravitational pull of attraction due to M takes the lead to make m move towards it AUTOMATICALLY as the gravitational pull of attraction due to 16 M vanishes i.e., a minimum KE or velocity has to be imparted to m from surface of 16 M such that it is just able to OVERCOME the gravitational pull of 16M. By law of conservation of energy `rArr 1/2mv^2+[-(G(16M)M)/(2a)-(GMM)/(8a)]+[-(GMm)/(2a)-(G(16M)m)/(8a)]=0` `rArr 1/2mv^2-(GMm)/(8a)(45)rArr v=3/2sqrt((5GM)/a)` |
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