Assertion : A tennis ball bounces higher on hills than in plains.… - Vidyadip

MCQ

$Assertion$ : A tennis ball bounces higher on hills than in plains.
$Reason$ : Acceleration due to gravity on the hill is greater than that on the surface of earth

A
If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
B
If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
✓
If the Assertion is correct but Reason is incorrect.
D
If both the Assertion and Reason are incorrect.

✓

Answer

Correct option: C.

If the Assertion is correct but Reason is incorrect.

c
$\begin{array}{l}
Suppose\,that\,the\,tennis\,ball\,bounces\,\\
with\,a\,velocity\,u.\,It\,will\,go\,up,\,its\,velocity\\
becomes\,zero.\,If\,h\,is\,the\,hgight\,up\,to\,which\\
it\,rises\,on\,the\,hill,\,then\\
\,\,\,\,\,\,\,\,\,\,\,\,{\left( 0 \right)^2} - {u^2} = 2\left( { - g'} \right)h\\
Where\,g'\,is\,acceleration\,due\,to\,gravity\,\\
on\,the\,hill.
\end{array}$

$\begin{array}{l}
\therefore h = \frac{{{u^2}}}{{2g'}}\\
{\rm{since}},\,the\,accleration\,due\,to\,gravity\,on\\
the\,hill\,\left( {g'} \right)\,is\,less\,than\,that\,on\,earth\,\\
\left( {effect\,of\,height} \right),\,it\,follows\,that\,tennis\\
ball\,will\,bounce\,higher\,on\,hills\,than\,in\,\\
plains.
\end{array}$

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