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Assertion: The given equation x = x(0) +...

Assertion: The given equation `x = x_(0) + u_(0)t + (1)/(2) at^(2)` is dimensionsally correct, where x is the distance travelled by a particle in time t , initial position `x_(0) ` initial velocity `u_(0)` and uniform acceleration a is along the direction of motion.
Reason: Dimensional analysis can be used for cheking the dimensional consistency or homogenetly of the equation.

A

if both assertion and reason are true reason is the correct explanation of assertion.

B

If both assertion and reason are true but reason is not the correct explanation fo assertion.

C

If assertion is true but reaso is false.

D

IF both assertion and reason are false.

Text Solution

Verified by Experts

The correct Answer is:
A
Given equation `x=x_(0)+u_(0)t+(1)/(2)at^(2)`.
The dimensions of each term may be written as
`[x]=[L],[x_(0)]=[L],[u_(0)t]=[LT^(-1)][T]=[L]`
`[((1)/(2))at^(2)]=[LT^(-2)][T^(2)]=[L]`
As each ter on the right hand side of this equation has the same dimension as left hand side of the equation, hence this equation is dimensionally correct.
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