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3-2.Motion in Plane
medium
The acceleration of a body in a non-uniform circular motion is $5\, ms^{-2}$. Which one of the following is correct?
AThe radial acceleration and the tangential accelerations are $3\, ms^{-2}$ and $4\, ms^{-2}$ respectively
BThe radial and the tangential accelerations are $2\, ms^{-2}$ and $3\, ms^{-2}$ respectively
CThe radial and the tangential accelerations are both $5\, ms^{-2}$.
DThe radial and the tangential acceleration are $5\, ms^{-2}$ and $3\, ms^{-2}$ respectively.
(AIIMS-2009)
Solution
$\begin{array}{l}
The\,acceleration\,of\,a\,body\,in\,a\,nonunifrom\\
cicular\,motion\,is\,the\,{\rm{resultant}}\,of\,the\,radial\\
and\,the\,t{\rm{angential}}\,{\rm{accelerations}}{\rm{.}}\\
{\rm{If}}\\
{{\rm{a}}_r} = 3m{s^{ – 2}}and\,{a_t} = 4m{s^{ – 2}}\\
then,\,a = \sqrt {{a_r}^2 + {a_t}{\,^2}} = \sqrt {{{\left( 3 \right)}^2} + {{\left( 4 \right)}^2}} \\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \sqrt {9 + 16} = \sqrt {25} = 5m{s^{ – 2}}
\end{array}$
The\,acceleration\,of\,a\,body\,in\,a\,nonunifrom\\
cicular\,motion\,is\,the\,{\rm{resultant}}\,of\,the\,radial\\
and\,the\,t{\rm{angential}}\,{\rm{accelerations}}{\rm{.}}\\
{\rm{If}}\\
{{\rm{a}}_r} = 3m{s^{ – 2}}and\,{a_t} = 4m{s^{ – 2}}\\
then,\,a = \sqrt {{a_r}^2 + {a_t}{\,^2}} = \sqrt {{{\left( 3 \right)}^2} + {{\left( 4 \right)}^2}} \\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \sqrt {9 + 16} = \sqrt {25} = 5m{s^{ – 2}}
\end{array}$
Standard 11
Physics
