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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 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

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Solution

The correct option is A
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(a) For particle P, motion between AC will be an accelerated one while between CB a retarded one. But in any case horizontal component of its 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 for both the particles are equal. Therefore, $t_{p}$ < $t_{q}$ .

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Similar questions

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 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 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?

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

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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