Question

Given in the diagram OB = BA. The time taken to cover OB is $T_1$ and the time take to cover BA is $T_2$, then the ratio $T_1/T_2$ is

• A. = 1
• B. > 1
• C. < 1
• D. cannot be determined

Answer 1

The correct option is B > 1

By the helps of given figure

Consider a distance $K$ as shown from projectile path to $B$.

Consider the inclined place be absent.

Then

$\begin{array}{c}OP=OB\cos {30}^{\circ }-K\cos {60}^{\circ }\\ O{P}^{\prime }=2OB\cos {60}^{\circ }\\ P{P}^{\prime }=OB\cos {30}^{\circ }+K\cos {60}^{\circ }\end{array}$

Since the horizontal component of velocity remains constant. time taken to cover layer distance is larger.

since $P{P}^{\prime }>OP$

Time taken to travel $OB<TimetakentocoverBA$ along the inclined plane.

so, $>1$

Hence, the option $B$ is the correct answer.