Radius of Gyration

Q.

The radius of gyration of uniform rod of length L and mass M about an axis passing through its centre and perpendicular to its length is

1. 

2. 

3. 

4. 

Q.

A ring is rolling on a horizontal surface without slipping. Find the ratio of translation K.E. to rotational K.E. of ring.

1. 1 : 2

2. 2 : 1

3. 4 : 1

4. 1 : 1

Q. The moment of inertia of a solid sphere about an axis passing through the centre of gravity is $\frac{2}{5}M{R}^2$; then its radius of gyration about a parallel axis at a distance $2R$ from first axis is

1. $5R$
2. $\sqrt{\frac{22}{5}}R$
3. $\frac{5}{2}R$
4. $\sqrt{\frac{12}{5}}R$

Q. A rigid horizontal smooth rod `AB` of mass `0.75 kg` and length `40 cm` can rotate freely about a fixed vertical axis through its mid point `O`. Two rings each of mass `1 kg` are initially at rest at a distance of `10 cm` from `O` on either side of the rod. The rod is set in rotation with an angular velocity of `30` radian per second. Find the velocity of each ring along the length of the rod in `m/s` when they reach the ends

Q.

The surface density $\left(\frac{mass}{area}\right)$ of a circular disc of radius a depends on the distance from the centre as $\rho \left(r\right)$ = $A+Br$. Find its moment of inertia about the line perpendicular to the plane of the disc through its centre

1. 

2. 

3. 

4. 

Q. The radius of gyration of a uniform rod of length $L$, about an axis passing through its centre of mass and perpendicular to it's length is:

1. $\frac{L}{2\sqrt{3}}$
2. $\frac{L^2}{12}$
3. $\frac{L}{\sqrt{3}}$
4. $\frac{L}{\sqrt{2}}$

Q. A particle of mass m is released from a height R from the surface of earth. When it reaches the earths surface, it enters a tunnel leading to its centre. Its speed at the centre is

Q.

Moment of inertia of two spheres of equal radii are equal. One of the spheres is solid and has the mass 5 kg and the other is a hollow sphere. What is the mass of hollow sphere?

1. 5 kg

2. 2/5 kg

3. 2/3 kg

4. 3 kg

Q. A spherical shell first rolls and then slips down an incline plane the ratio of its acceleration in two cases will be

Q. Three identical rods each having mass m and length l are fixed in the form of an equilateral triangle. The moment of inertia of the system about the vertex and perpendicular to the plane of the triangle is (1) ml^2/2 (2) 3ml^2/2 (3) ml^2/12 (4) ml^2/3

Q.

Suppose you place a sphere of mass m and radius rinside a smooth, heavy hemispherical bowl of radius of 37r placed on a horizontal table. If the sphere is given a small displacement, what is its period of oscillation?

1. 

2. 

3. 

4. 

Q. Find the ratio of radius of gyration about natural axis of a circular disk to that of a circular ring each having same mass and same radius.

Q. Radius of gyration of a uniform disc about a line perpendicular to the plane of disc is equal to its radius $R$. If the distance of the line from the center is $\frac{R}{\sqrt{x}},$ find the value of $x$.

1. $2$
2. $4$
3. $1$
4. $8$

Q. The ratio of radius of gyration of a solid sphere and hollow sphere of the same mass and radius about a tangential axis is

1. $\sqrt{7}:\sqrt{3}$
2. $5:\sqrt{21}$
3. $\sqrt{5}:\sqrt{6}$
4. $\sqrt{21}:5$

Q. there is a cricket bat which is cut form its centre of mass perpendicular to longitudinal axis ofbat.which part ofbat wil have more mass? Part having the handle or part opp to it

Q. (a) Centre of gravity (C.G) of a body is the point at which the weight of the body acts (b) Centre of mass coincides with the centre of gravity if the earth is assumed to have infinitely large radius (c) To evaluate the gravitational field intensity due to any body at an external point, the entire mass of the body can be considered to be concentrated at its C.G. (d) The radius of gyration of any body rotating about an axis is the length of the perpendicular dropped from the C.G. of the body to the axis Which one of the following pairs of statements is correct ?

Q.

Define centre of gravity.

Q. four particles each of mass m are placed at the corners of a square of side length l. the radius of gyration of system about the axis perpendicular to the square and passing through its centre is

Q. 58. A car is moving on circular path and take a turn . If r1 and r2 be the reaction on inner and outer wheel respectively than why r2 is greater than r1?

Q. A paraboloid shaped solid object is formed by rotation on parabola y=2x^2 about y axis as shown . If height of body is h then position of center of mass from origin is

Q.

Consider the statements A and B and choose the appropriate option from those given below.

A: The position of centre of mass of a body is independent of acceleration due to gravity.

B: The center of mass of a body always lies within the boundaries.

1. A true, B false

2. A false, B true

3. A true, B true

4. A false, B false

Q.

On what factors does the radius of gyration depend?

Q. Find the radius of gyration of a uniform disc of radius $R$ and mass $M$ about its edge and perpendicular to the disc.

1. $\frac{\sqrt{5}}{2}R$
2. $\frac{3}{2}R$
3. $\sqrt{\frac{3}{2}}R$
4. $\frac{9}{2}R$

Q. The moment of inertia of a system of four rods eachof length e and mass m making a square about theaxis AA shown in figure will be (axis AA is in theplane of the square)A :AT AA passes through one of the vertex parallel to the diagobal of sqare

Q. The radius of gyration of a uniform rod of length $L$, about an axis passing through its centre of mass and perpendicular to it's length is:

1. $\frac{L}{2\sqrt{3}}$
2. $\frac{L^2}{12}$
3. $\frac{L}{\sqrt{3}}$
4. $\frac{L}{\sqrt{2}}$

Q. Two identical solid sphere each of mass $m=5\text{kg}$ and radius $r=1\text{m}$ are joined at the ends of a light rod of length $l=2\text{m}$ to form a system as shown in figure. Radius of gyration of the system about an axis perpendicular to the length of rod and passing through center of mass of system is

1. $\sqrt{44}\text{m}$
2. $\sqrt{2.4}\text{m}$
3. $\sqrt{3.2}\text{m}$
4. $\sqrt{4.4}\text{m}$

Q. Find the ratio of radius of gyration about natural axis of a circular disk to that of a circular ring each having same mass and same radius.

1. $1:1$
2. $2:1$
3. $1:\sqrt{2}$
4. $\sqrt{2}:1$

Q. Three particles each 1kgmass are placed at the corners of a right angled triangle AOB, O being the origin of the coordinate system (OA OB) along positive x direction and positive y-direction.The position vector of the centre of mass? if OA=OB=1mt(in meters)

Q. Two discs each having moment of inertia $5kg$ $m^2$ about its central axis, rotating with speeds $10rad{s}^{-1}$ and $10rad$ $s^{-1}$, are brought in contact face to face with their axes of rotation coincided. The loss of kinetic energy in the process is:

1. $5J$
2. $125J$
3. $0J$
4. $2J$

Q. if a constant couple of 500 Nm turns a wheel of moment of inertia 100 kg m square about an axis through its centre the angular velocity gained is?