Question

23. A body is allowed to slide from the top along a
smooth inclined plane of length 5m at an angle
of inclination 30°. If g= 10ms 2, time taken by
the body to reach the bottom of the plane is


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Answer 1

Given:

A body is allowed to slide from the top along a smooth inclined plane of length 5m at an angle of inclination 30°.

To find:

Time taken by body to reach the bottom of the incline.

Calculation:

Considering the contact between body and inclined plane to be frictionless, we can say that the net acceleration of the body is:

$\therefore \: a_{net} = g \sin( \theta)$

$\implies \: a_{net} = g \sin( {30}^{ \circ} )$

$\implies \: a_{net} = g \times \dfrac{1}{2}$

$\implies \: a_{net} = 10 \times \dfrac{1}{2}$

$\implies \: a_{net} = 5 \: m {s}^{ - 1}$

Now , applying 2nd equation of kinematics:

$\therefore \: s = ut + \dfrac{1}{2}( a_{net}) {t}^{2}$

$\implies \: 5= (0)t + \dfrac{1}{2}(5) {t}^{2}$

$\implies \: 5= \dfrac{1}{2}(5) {t}^{2}$

$\implies \: {t}^{2} = 2$

$\implies \: t= \sqrt{2}$

$\implies \: t \approx 1.414 \: sec$

So, time taken to reach the bottom of incline is approximately 1.414 seconds