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### 12th Grade > Physics

## KINEMATICS MCQs

### Circular Kinematics

Total Questions : 41
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**3**of 5 pages**A balloon starts rising from the surface of the Earth. The ascension rate is constant and equal to v**

__Question 21.___{o}. Due to the wind the balloon gathers the horizontal velocity component v

_{x}=ay, where a is a constant and y is the height of ascent. Find the total, tangential, and normal accelerations of the balloon.

**Answer: Option C. ->**ar=av0;at=a2y√1+a2y2v20;aN=av0 ⎷(1+a2y2v20)

:

C

The path of the balloon will look something like this

After t sec ballon would have gone a height of v0tthen at that very instance the balloon's vx will be

vx=av0t⇒ax=av0

Vy=v0

ay=0

ar=totalacceleration=av0.......(1)

vtangentical is actually the resultant velocity

⇒vt=√v20+(av0t)2

⇒vt=v0√1+a2t2

at=dvtdt=v0a2t√1+a2t2⇒a2y√1+(ayv0)2

Now we know a2t+a2N=a2r

⇒v20a4t2(1+a2t2)+a2N=a2v20

aN=√v20a4t2−v20a4t2(1+a2t2)

aN=av0√1+a2t2−a2t2(1+a2t2)

aN=av0√1+a2t2

⇒av0√1+(ayv0)2

**A hollow vertical cylinder of radius R and height h has smooth internal surface. A small particle is placed in contact with the inner side of the upper rim at a point P. It is given a horizontal speed v**

__Question 22.___{o}tangential to rim. It leaves the lower rim at point Q, vertically below P. The number of revolutions made by the particle will

**Answer: Option D. ->**v02πR(√2hg)

:

D

since the body has no initial velocity in the vertical direction.

az=-g, vertical displacement z=-h.

∴z=at+12at2

⇒−h=0+12(−g)t2

⇒T=√2hg time taken to reach the bottom

let,t be the time taken to complete one revolution.

Then t=2πRv0

∴ number of revolution=Tt=√2hg2πRv0=v02πR√2hg

**Answer: Option D. ->**14 m/s

:

D

Vmax=√μrg=√0.2×100×9.8=14m/s

**Answer: Option D. ->**14 m/s2

:

D

S=t3+5

Speed,v=dsdt=3t2 and rate of change of speed =dvdt=6t

∴ tangential acceleration at t=2S,at = 6 × 2=12m/s2

Att=2s,v=3(2)2=12m/s2

∴ centripetal acceleration,

=v2R=14420m/s2

∴ net acceleration=√a2t+a2i≈14m/s2

**Answer: Option D. ->**d

:

D

The net acceleration is always directed between radially inward and tangential direction.

**Answer: Option A. ->**√rFm

:

A

F=mv2r⇒v=√rFm

**Answer: Option B. ->**-2m/s2

**Answer: Option C. ->**km/hr

**Answer: Option A. ->**10m/s