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Standard XII

Physics

Projectile Time, Height and Range

A particle is...

Question

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

$t_{P} < t_{Q}$

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$t_{P} = t_{Q}$

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$t_{P} > t_{Q}$

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All of these

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Solution

The correct option is A
$t_{P} < t_{Q}$

For particle P, motion between A and C will be an accelerated one while between C and B a retarded one. But in any case horizontal component of it’s velocity will be greater than or equal to v on the other hand in case of particle Q, it is always equal to v. horizontal displacement of both the particles are equal, so $t_{P} < t_{Q}$ .

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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 $t_{p}$ and $t_{q}$ be the respective times taken by P and Q to reach the point B. Then

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 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:

Q. A particle

P

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

A

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

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 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}

and

t_{Q}

be the respective times taken by P and Q to reach the point B. Then?

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

Time taken by p is

a) less than Q

b) greater than Q

c)equal to Q

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