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A bead of mass m slides along a straight frictionless rigid wire rotating in a horizontal plane with a constant angular speed ω. The axis of rotation is perpendicular to the wire and passes through one end of the wire. If r is the distance of the mass from the axis of rotation and v is its speed, then the magnitude of the Coriolis force is
A
$$\frac{{m{v^2}}}{r}$$
B
$$\frac{{2m{v^2}}}{r}$$
C
mvω
D
2mvω
Correct Answer:
2mvω
A rigid frictionless rod rotates anticlockwise in a vertical plane with angular velocity $$\overrightarrow \omega $$. A bead of mass m moves outward along the rod with constant velocity $$\overrightarrow {{u_0}} $$ . The bead will experience a coriolis force
A
$$2{m_0}u\omega \hat \theta $$
B
$$ - 2m{u_0}\omega \hat \theta $$
C
$$4m{u_0}\omega \hat \theta $$
D
$$ - m{u_0}\omega \hat \theta $$
A rigid body is rotating about an axis. One force F1 acts on the body such that its vector passes through the axis of rotation. Another force F2 acts on it such that it is perpendicular to the axis of rotation and at a point 5cm from the axis. This force F2 is perpendicular to the radius vector at its point of application. Find the net torque on the body. Let F1 = 10N & F2= 5N.
A
0
B
10.25Nm
C
0.25Nm
D
10Nm
A line is perpendicular to profile plane, the perpendicular distance from 1st end of the line to vertical plane is 20 cm and perpendicular distance of 2nd end of line to horizontal plane is 10 cm. What is the distance from 1st end of line to vertical plane?
A
15 cm
B
20 cm
C
10 cm
D
Can’t say
A mass m is constrained to move on a horizontal frictionless surface. It is set in circular motion with radius r
0
and angular speed ω
0
by an applied force $$\overrightarrow {\bf{F}} $$ communicated through an inextensible thread that passesthrough a hole on the surface as shown in figure given below. Then, this force is suddenly doubled.
The magnitude of the radial velocity of the mass
A
increases till mass falls into hole
B
decreases till mass falls into hole
C
remains constant
D
becomes zero at radius r<sub>1</sub>, where 0 1 0
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
A circular hoop of mass M and radius a rolls without slipping with constant angular speed ω along the horizontal X-axis in the X-Y plane. When the hoop is at a distance d = $$\sqrt 2 $$ a from the origin, the magnitude of the total angular momentum of the hoop about the origin is
A
Ma<sup>2</sup>ω
B
$$\sqrt 2 $$ Ma<sup>2</sup>ω
C
2Ma<sup>2</sup>ω
D
3Ma<sup>2</sup>ω
A line of 12 cm length is perpendicular to profile plane and the least distance from this line to profile plane is 6 cm. This is at a distance of 4 cm from the vertical plane and 5 cm from the horizontal plane. What is distance from the point on line far away from the profile plane to profile plane?
A
12 cm
B
9 cm
C
18 cm
D
6 cm
A line is perpendicular to horizontal plane, the perpendicular distance from the line to vertical plane is 8 inches and perpendicular distance from the line to profile plane is 5 inches. What is the distance from the line to vertical reference line if it is viewed from front view?
A
8 inches
B
5 inches
C
3 inches
D
0 inches
A line is perpendicular to profile plane, the perpendicular distance from the line to vertical plane is 10 cm and perpendicular distance from the line to horizontal plane is 5 cm. What is the distance from the line to vertical reference line if it is viewed from a side view?
A
10 cm
B
5 cm
C
7.5 cm
D
0 cm
Which of the statements given are correct?
1. Coriolis effect is zero at the Equator.
2. Coriolis effect is more towards the Poles.
3. Coriolis effects are related to the decreasing rotational velocity with increasing latitudes.
4. Coriolis effects are related to the increasing rotational velocity with increasing latitudes.
A
1, 2 and 3
B
1 and 3 only
C
1, 2 and 4
D
2 and 5 only
