MCQ
With the usual notations, the following equation $S_t=u+\frac{1}{2} a(2 t-1)$ is
- AOnly numerically correct
- BOnly dimensionally correct
- ✓Both numerically and dimensionally correct
- DNeither numerically nor dimensionally correct
✓
Answer
Correct option: C.
Both numerically and dimensionally correct
(c) We can derive this equation from equations of motion so it is numerically correct.
$S_t=\text { distance travelled in } t \text { second }=\frac{\text {Distance }}{\text { time }}$
$=\left[L T^{-1}\right] \\u=\text { velocity }$
$=\left[L T^{-1}\right] \text {and } \frac{1}{2} a(2 t-1)$
$=\left[L T^{-1}\right]$
As dimensions of each term inthe given equation are same, hence equation is dimensionally correct also.
$S_t=\text { distance travelled in } t \text { second }=\frac{\text {Distance }}{\text { time }}$
$=\left[L T^{-1}\right] \\u=\text { velocity }$
$=\left[L T^{-1}\right] \text {and } \frac{1}{2} a(2 t-1)$
$=\left[L T^{-1}\right]$
As dimensions of each term inthe given equation are same, hence equation is dimensionally correct also.
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