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What is the principle value of sec^(−1)(...

What is the principle value of `sec^(−1)(2/(√3))`.
a) π/6
b) π/3
c) π/4
d) π/2

Text Solution

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When slipping ceases, the linear speeds of the points of contact of the two cylinders will be equal. If the `omega_1 and omega_2` be the respective angular speeds, we have
`omega'_1r_1=omega'_2=r_2`……….i
The change in the angular speed is brought about by the frictioN/Al force which acts as long as the slipping exists. If this force f acts for a time t, the torque on the first cylinder is `fr_1` and that on the second is `fr_2`. Assuming `omega_1r_1gtomega_2r_2` the corresponding angular impluses are `-fr_1t and fr_2t`. We therefore have
`-fr_1t=I_1(omega'_1-omega_1)`
`and fr_2t=I_2(omega'_2=omega_2)`
or `-I_1/r_1(omega'_1-omega_1)=I_2/r_2(omega'_2-omega_2)`........ii
Solving i and ii
`omega'_1=(I_1omega_1r_2+I_2omega_2r_1)/(I_2r_1^2+I_1r_2^2)r_2 and omega'_2=(I_1omega_1r_2+I_2 omega_2r_1)/(I_2r_1^2+I_1r_2^2)`
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