Question

A sphere of radius R comes in contact with wedge moving as shown. The point of
contact is R/5 from the ground as shown in the figure. Velocity of wedge is
20 m/s, then the velocity of the sphere at this instant will be
(A) 20 m/s
(B) 10 m/s
(C) 5 m/s
(D) 15 m/s
​

Answer 1

SOLUTION

Assume for the moment that R= 5(it doesn't matter for the slope),

so the circle is given by x^2+y^2=25

Because height= R/5

We are looking for the slope of the tangent line through the point with y=-4

which is (-3,-4)

Now the slope is given by = -x/y= -3/4

=) Now, given a velocity of 20m/s to the left

We know that the sphere will have a velocity of 3/4× 20m/s

=) 15m/s

hope it helps ✔️

Answer 2

Thus the velocity of sphere at this instant will be 15 m/s.

Option (D) is correct.

Explanation:

We are give that:

• Radius of sphere = R
• Point of contact = R / 5
• Velocity of wedge = 20 m/s

Solution:

The angle cos θ = 4R / 5 / R = 0.8

v1 / v2 = tan θ = tan 37° = 3 /4

v1 =  3/4 v2

v1 = 3 / 4  x 20

v1 =  15 m/s

Thus the velocity of sphere at this instant will be 15 m/s.