A satellite is seen after every 8 hours. If it rotates opposite to that of the earth, what is its angular velocity about the centre of the earth? Assume the earth is perfectly spherical and the satellite is in the equatorial plane.

A hollow rod has frictionless inner walls. Inside the rod are two small spheres that are kept on either side of the centre of rod. The rod is rotated about its central axis which is perpendicular to the plane of rotation. If the rod had been rotated by an impulsive torque which gave it an instantaneous angular velocity of 5rad/s, what will be the angular velocity after some finite but long time ‘t’? Assume no external forces act on rod after the impulse. Also state what will happen to the spheres in the centre of the rod. The rod has a mass =2kg & length =10cm. The two spheres have a mass =1kg each.

A

2.5 rad/s, spheres will stay where they are as there is no friction to move them

B

0 rad/s, spheres will move outwards and decrease velocity of rod to zero

C

1.25 rad/s, spheres will move to opposite ends of rod

D

2.5 rad/s, spheres will move to opposite ends of rod

Assume that after every budding cycle, the parent organism becomes barren. And the daughter organism produced further gives rise to a new organism. After a period of 78 hours, how many fertile and barren organisms would be left if the initial number of organisms N0 = 2 (Assume that every budding cycle takes 2 hours)?

A

1 and 239-1 respectively

B

1 and 39 respectively

C

2 and 78 respectively

D

2 and 240-1 respectively

A rigid body is rotating about its centre of mass; fixed at origin with an angular velocity $$\overrightarrow \omega $$ and angular acceleration $$\overrightarrow \alpha $$. If the torque acting on it is $$\overrightarrow \tau $$ and its angular momentum is $$\overrightarrow {\bf{L}} $$, then the rate of change of its kinetic energy is

A

$$\frac{1}{2}\overrightarrow \tau \cdot \overrightarrow \omega $$

B

$$\frac{1}{2}\overrightarrow {\bf{L}} \cdot \overrightarrow \omega $$

C

$$\frac{1}{2}\left( {\overrightarrow \tau \cdot \overrightarrow \omega + \overrightarrow {\bf{L}} \cdot \overrightarrow \alpha } \right)$$

D

$$\frac{1}{2}\overrightarrow {\bf{L}} \cdot \overrightarrow \alpha $$

A horizontal platform is rotating with uniform angular velocity ω around the vertical axis passing through its centre. At some instant of time, a viscous liquid of mass m is dropped at the centre and is allowed to spread pout and finally fall. The angular velocity during this period ___________

A

Decreases continuously

B

Decreases initially and increases again

C

Remains unaltered

D

Increases continuously

The revelations of a satellite photograph of the earth are as follows:
1. the Southern hemisphere bulges slightly more than the Northern hemisphere
2. it is slightly pear shaped ellipsoid of rotation
3. the polar axis of the earth is slightly shorter than the equatorial axis
4. the equatorial circumference is about 40,000km
Which of the above statements are correct ?

A

1, 2 and 3

B

1, 2, 3 and 4

C

1, 2 and 4

D

2, 3 and 4

Assume that a satellite executes perfectly circular orbits around a perfectly circular sphere. The work done by the satellite in 1 complete revolution is _____

A

(1/2) x (G x m x M)/(R+h)

B

– (G x m x M)/(R+h)

C

– (1/2) x (G x m x M)/(R+h)

D

0

A thin circular ring of mass m and radius R is rotating about its axis with a constant angular velocityω. Two objects each of mass M are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity ω‘, which is equal to?

A

mω/(m+M)

B

mω/(m+2M)

C

((m+2m)ω)/m

D

((m-2M)ω)/((m+2M))

What is the force of gravity experienced by an object at the centre of the earth? (Assume that the earth is perfectly spherical)

A

0 g-force

B

1 g-force

C

9.81 g-force

D

10 g-force

A smooth sphere A is moving on a frictionless horizontal plane with angular speed ω and the centre of mass velocity u. It collides elastically and head on with an identical sphere B at rest. Neglect friction everywhere. After the collision, their angular speeds are ω(A) and ω(B) respectively. Then?

A

ωA is lesser than ωB

B

ωA=ωB

C

ωA=ω

D

ωB=ω

In the figure given below A and D are fixed points, link AB rotates at a uniform angular velocity of 900 rev/min ccw, find angular velocity of BC in rad/s. Rab = 100mm, Bc = 450, distance of E from BC = 100mm, Cf= 75mm, CD = 275mm, AD =250mm, perpendicular DF = 17mm, perpendicular BE = 250mm.

A

28.3

B

2 8.7

C

29.4

D

25.3