In U.C.M., when time interval δ→0 , the angle between change in velocity δv and linear velocity (v) will be

MHT CET · Physics · Motion In Two Dimensions

In U.C.M., when time interval $δ \to 0$ , the angle between change in velocity $(δ v)$ and linear velocity (v) will be

A $0^{o}$
B $90^{o}$
C $180^{o}$
D $45^{o}$

Verified Solution

Answer & Solution

Correct Answer

(B) $90^{o}$

Step-by-step Solution

Detailed explanation

The direction of change in velocity

(δ v)

is given by

ϕ = \frac{180^{o} - θ}{2} = 90^{o} - \frac{θ}{2}

…. (i)
This can be shown graphically as

For small interval i.e.

δ t \to 0

, then angle between

v_{1}

and

v_{2}

is very small i.e.,

θ \approx 0^{o}

.
So, from Eq. (i) we get

ϕ = 90^{o}

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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