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Consider a disc rotating in the horizont...

Consider a disc rotating in the horizontal plane with a constant angular speed `omega` about its centre O . The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebbles P and Q are simultaneously projected at an angle towards R. The velocity of projection is in the y-z plane and is same for both pebbles with respect to the disc. Assume that (i) they land back on the disc before the disc has completed `(1)/(8)` rotation, (ii) their range is less than half the disc radius, and (iii) w remains constant throughout. Then

A

`p` lands in the shaded region and `Q` in the unshaded region.

B

`P` landa in the unshaded region and `Q` in the shaded region.

C

Both `P` and `Q` land in the unshaded region.

D

Both `P` and `Q` land in the shaded region.

Text Solution

Verified by Experts

The correct Answer is:
C
The `x - coordinate` distance of `P = ` P = v_(x) xx t = omega R xx (pi)/(4omega) = (pi R)/(4)`
This horizontal distance travelled will be greater than any point on the disc between `O` and `P`. Therfore the landing will be in unshaded area . In the same way , the horizontal distance travelled by `Q` is always less than that of any point between `O` and `R` . Therfore the landing will be in unshaded area.
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Knowledge Check

  • Consider a disc rotating in the horizontal plane with a constant angular speed omega about its center O. The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in figure. When the disc is in the orientation as shown, two pebbles P and Q are simultaneously projected at an angle towards R. The velocity of projection in the y-z plane and is same for both pebbles with respect to the disc. Assume that (i) they land back on the disc before the disc has completed 1//8 rotation, (ii) their range is less than half the disc radius, and (iii) omega remains constant throughout. Then

    A
    P lands in the shaded region and Q in the unshaded region.
    B
    P lands in the unshaded region and Q in the shaded region.
    C
    Both P and Q land in the unshaded region.
    D
    Both P and Q land in the shaded region.

  • Consider a disc rotating in the horizontal plane with a constant angu lar speed omega about its centre O. the disc has shaded region on one side of the diameter and an unshaded region on the other side as shown in Fig. 5.111. when the disc is in the orientation as shown, two pebbles P and Q are simu ltaneously projected at an angle towards R. the velocity of projection in the y-z plane and is same for both pebbles with respect to the disc. Assume that i they land back on the disc before the disc has completed 1/8 rotation, ii their range is less than half the disc radus, and iii omega reamisn constant throughout. then

    A
    P lands in the shaded region and Q in the unshaded region.
    B
    P lands in the unshaded region and Q in the shaded region.
    C
    Both P and Q land in the unshaded region
    D
    Both P and Q land in the shaded region

  • Consider a sisc rotating in the horizontal plane with a constant angular speed omega about its centre (O). The disc has a shade region on one side of the diameter and an unshaded region on the other side as shown in the Fig. 2 (CF) . 37, When pebbles (P) and (Q) ar simultaneously proected at an angle towards. (R ). The velocity of projection is in the y-z plane and is same for both pebbles with respect to the disc . Assume that (i) they lang back on the disc beforec teh disc has completed /8 rotation, (ii) their range is less than half the disc radius, and (iii), omega remains constant throughout. Then .

    A
    (P) lands in the shaded ragion and (Q) in the unshaded region
    B
    (P) lands in the unshaded region and (Q) in the saded region
    C
    Both (P) and (Q) land in the unshaded region
    D
    Both (P) and (Q) land in the shaded region

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