UPSEE Solved Model Paper 7

Assume that the body slides down the plane from rest, i.e. u = 0. Let 'h' be the total distance (length) of the inclined plane.
Case I: The body covers

h

4

distance in time t = 2 s
Using the second equation of motion: S = ut +

1

2

at2, where
S =

h

4

; distance covered
t = 2 s: time taken
u = 0: initial velocity
a: acceleration of the block
⇒

h

4

= 0 +

1

2

a×22
⇒ h = 8a ... (i)
Case Ii: The body covers the distance of the complete inclined planeDistance covered, S = h; f = time taken and initial velocity, u = 0.
Using the same equation of motion, we obtain
h = 0 +

1

2

at2 ... (ii)
Equating eqs. (i) and (ii), we get
8a =

1

2

at2
⇒ t' = √16s = 4s
Therefore, time taken by the body to cover the total distance of the inclined plane is 4 s.
Hence, option 'A' is correct.