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A ball rolls of the top fi a strair way ...

A ball rolls of the top fi a strair way with horizonntal velocity of magnitude ` 1. 8 ms^(-1)`. The steps are ` 0.20 m` high and ` 0.02 m` wide , Which step will the ball it first ? ( g = 10 m//s^@)`.

A

(a) both Assertion and Reason are true and the Reason is correct explanation of the Assertion .

B

(b )both Assertion and Reason are true but the Reason is not a correct explanation of the Assertion.

C

(C ) Assertion is true but the Reason is false.

D

(d) both Assertion and Reason are false.

Text Solution

Verified by Experts

The correct Answer is:
C
Let the ball strike the ` nth` step in time (t), where vertical height if each step is (h) and horizonta length of each step is (x). So ,
` nh = 1/2 gt^2 ` or ` t= sqrt (2 nh)/2`
Now ` ut = nx `or ` n= (ut)/x = u/x sqrt(2 nh)/g`
Squating both the sides, we have
` n=( 2 u^2 h)/( x^2 g) = (2 xx (1.8)^2 xx 0.2)/((0.2)^2 xx 10) = 3 . 24`
`~~ 4 (Fourth step)`.
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