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Calculate the centripetal acceleration of moon towards the earth

Answer» <html><body><p></p>Solution :The centripetal acceleration is given by `a = (v^2)/(r )` .This expression <a href="https://interviewquestions.tuteehub.com/tag/explicitlybrbr-2628242" style="font-weight:bold;" target="_blank" title="Click to know more about EXPLICITLY">EXPLICITLY</a> depends on Moon.s speed which is nontrivial. We can work with the formula <br/>`omega^2 R_m = a_m` <br/> `a_m`is centripetal acceleration of the Moon due to Earth.s <a href="https://interviewquestions.tuteehub.com/tag/gravity-18707" style="font-weight:bold;" target="_blank" title="Click to know more about GRAVITY">GRAVITY</a>. <br/>`omega `is angular <a href="https://interviewquestions.tuteehub.com/tag/velocity-1444512" style="font-weight:bold;" target="_blank" title="Click to know more about VELOCITY">VELOCITY</a><br/>`R_m`is the distance between Earth and the Moon, which is 60 times the radius of the Earth. <br/>`R_m = 60 R = 60 xx 6.4 xx 10^6 = 384 xx 10^6 m`<br/>As we know the angular velocity `omega = (2pi)/(T)` and <br/> `T = 27. 3 days = 27.3 xx 24 xx 60 xx 60 sec= 2.358 xx 10^6 sec ` <br/>By substituting these values in the formula for acceleration <br/>`a_m = ((4pi^2) (384 xx 10^6) )/((2.358 xx 10^6)^2) = 0.00272 <a href="https://interviewquestions.tuteehub.com/tag/ms-549331" style="font-weight:bold;" target="_blank" title="Click to know more about MS">MS</a>^(-2)` <br/>The centripetal acceleration of Moon towards the Earth is` 0.00272 ms^(-2)`</body></html>


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