**INDUSTRY AND COMPANY AWARENESS (ICA)**

Question

:

C

â†’r=RcosÎ¸^j

âˆ´dâ†’rdt=âˆ’RsinÎ¸dÎ¸dt^i+RcosÎ¸dÎ¸dt^j

â‡’â†’v=âˆ’RÏ‰sinÎ¸^i+RÏ‰cosÎ¸^j

(asÏ‰=dÎ¸dtanddâ†’rdt=â†’v)

â‡’dâ†’vdt=â†’a=RÏ‰cosÎ¸dÎ¸dt^i+RÏ‰(âˆ’sinÎ¸)dÎ¸dt^j

â‡’dsdtâ‰¡dÎ¸rdt=rdÎ¸dt=rÏ‰

âˆ´Ï‰ordÎ¸dtisconstant

âˆ´â†’v=âˆ’RÏ‰2cosÎ¸^iâˆ’RÏ‰2sinÎ¸^j

Substituting Ï‰=vR

â†’a=âˆ’v2RcosÎ¸^iâˆ’âˆ’v2RsinÎ¸^j

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For a particle in uniform circular motion the acceleration â†’a at a point P(R,Î¸)on the circle of radius R is (here Î¸ is measured from the x-axis)

**Answer: Option C**

:

C

â†’r=RcosÎ¸^j

âˆ´dâ†’rdt=âˆ’RsinÎ¸dÎ¸dt^i+RcosÎ¸dÎ¸dt^j

â‡’â†’v=âˆ’RÏ‰sinÎ¸^i+RÏ‰cosÎ¸^j

(asÏ‰=dÎ¸dtanddâ†’rdt=â†’v)

â‡’dâ†’vdt=â†’a=RÏ‰cosÎ¸dÎ¸dt^i+RÏ‰(âˆ’sinÎ¸)dÎ¸dt^j

â‡’dsdtâ‰¡dÎ¸rdt=rdÎ¸dt=rÏ‰

âˆ´Ï‰ordÎ¸dtisconstant

âˆ´â†’v=âˆ’RÏ‰2cosÎ¸^iâˆ’RÏ‰2sinÎ¸^j

Substituting Ï‰=vR

â†’a=âˆ’v2RcosÎ¸^iâˆ’âˆ’v2RsinÎ¸^j

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