JEE MAIN - Physics (2012 - No. 23)
Two cars of masses m1 and m2 are moving in circles of radii r1 and r2, respectively. Their speeds are such that they make complete circles in the same time t. The ratio of their centripetal acceleration is
m1r1 : m2r2
m1 : m2
r1 : r2
1 : 1
Explanation
We know, $$a = r\,{w^2} = r \times {\left( {{{2\pi } \over T}} \right)^2}$$
Given, $${T_1} = {T_2} = T$$
$${a_1} = {r_1} \times {\left( {{{2\pi } \over T}} \right)^2}$$
$${a_2} = {r_2} \times {\left( {{{2\pi } \over T}} \right)^2}$$
$$\therefore$$ $${{{a_1}} \over {{a_2}}} = {{{r_1}} \over {{r_2}}}$$
Given, $${T_1} = {T_2} = T$$
$${a_1} = {r_1} \times {\left( {{{2\pi } \over T}} \right)^2}$$
$${a_2} = {r_2} \times {\left( {{{2\pi } \over T}} \right)^2}$$
$$\therefore$$ $${{{a_1}} \over {{a_2}}} = {{{r_1}} \over {{r_2}}}$$
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