A solid sphere rolls down an inclined plane with an acceleration g/2. What is the angle of inclination of inclined plane?

Solution

The acceleration of sphere rolling down an inclined plane is given by,

straight alpha equals fraction numerator straight g space sin space straight theta over denominator 1 plus begin display style straight I over mr squared end style end fraction

For solid sphere,

space space space space straight I equals 2 over 5 mr squared

therefore space space space space space space space space space space straight g over 2 equals fraction numerator straight g space s i n space straight theta over denominator 1 plus begin display style 2 over 5 end style end fraction equals 5 over 7 space straight g space s i n space straight theta rightwards double arrow space space space space s i n space straight theta space equals space 7 over 10 equals 0.7 rightwards double arrow space space space space space space space space space space straight theta space equals space space s i n to the power of negative 1 end exponent 0.7

This is the required angle of inclination of the inclined plane.

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