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Byju's Answer

Standard XII

Physics

Projectile Time, Height and Range

A particle P ...

Question

A particle P is sliding down a frictionless hemispherical bowl. It passes the point A at t = 0. At this instant of time, the horizontal component of its velocity is v. A bead Q of the same mass as P is ejected from A at t = 0 along the horizontal string AB with speed v. Friction between the bead and the string may be neglected. Let t_P and t_Q be the respective times taken by P and Q to reach the point B. Then:

t_{p} < t_{Q}

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t_{p} = t_{Q}

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t_{p} > t_{Q}

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\frac{t_{p}}{t_{Q}} = \frac{L e n g t h o f a r c A C B}{L e n g t h o f c h o r d A B}

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Solution

The correct option is A $t_{p} < t_{Q}$
As the particle P moves from A to C, its horizontal velocity increases from v. Again the horizontal velocity decreases to v as P moves form C to B. So the horizontal velocity of P remains greater than or equal to v. But the horizontal velocity of bead Q remains constant equal to v. For same horizontal displacement AB, P takes smaller time than Q i.e.,
$t_{p} < t_{Q}$ .

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A particle is sliding down a frictionless hemispherical bowl. It passes the point A at t=0. At this instant of time, the horizontal component of its velocity is v. A bead Q of the same mass as P is ejected from A at t =0 along the horizontal string AB (see figure) with the speed v. Friction between the bead and the string may be neglected. Let $t_{P}$ and $t_{Q}$ be the respective time taken by P and Q to reach the point B. Then

Q. A particle

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is sliding down a frictionless hemispherical bowl. It passes the point

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t = 0

. At this instant of time, the horizontal component of its velocity is

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A

bead

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of the same mass as

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is ejected from

A

t = 0

along the horizontal string

AB

(see figure) with the speed

v

. Friction between the bead and the string may be neglected. Let

t_{P}

and

t_{Q}

be the respective time taken by

P

and

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Q. A particle P is sliding down a frictionless hemispherical bowl. It passes the point A at

t = 0

. At this instant of time, the horizontal component of its velocity is v. A bead Q of the same mass as P is ejected from A at

t = 0

along the horizonal string AB, with the speed v. Friction between the bead and the string may be neglected. Let

t_{P}

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A particle P is sliding down a frictionless hemispherical bowl. It passes the point A at t = 0. At this instant of time, the horizontal component of its velocity is v. A bead Q of the same mass as P is ejected from A at t = 0 along the horizontal string AB, with a speed v. Friction between the bead and the string may be neglected. Let tp and tq be the respective times taken by P and Q to reach the point B. Then

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a) less than Q

b) greater than Q

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