Tag: centre of gravity

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Questions Related to centre of gravity

Multiple choice physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

What is the center of mass of an object?

  1. The mean position of the mass in an object.

  2. The geometric center of an object.

  3. The furthest away position of the mass in an object.

  4. The same as the center of gravity.

  5. The closest position of the mass in an object.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The mass of the body is scattered equally in all space around the centre of mass. It is closer to the heavier regions of the object and hence need not be at the geometric centre. 

Options C and E don't make sense. 
It doesn't coincide with the centre of gravity for very large bodies like mountains.

Multiple choice physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

Which one of following statements related to center of gravity is incorrect?

  1. The center of gravity of an object is defined as point through which its whole weight appears to act.

  2. The center of gravity is sometimes confused with center of mass.

  3. The center of gravity always lies inside object.

  4. For an object placed in a uniform gravitational field, center of gravity coincides with center of mass.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A is the proper definition. In some bodies like hollow bodies, frames and rings, the center of gravity is at the geometric centre where the matter of the object is not present.

Multiple choice physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

The stability of a flexible body depends on:

  1. height of the center of gravity from the ground.

  2. base area of the body.

  3. shape of the body.

  4. all the above.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The stability of objects depends on the base, C.G and shape of the body. For a body to be the stable,

  1. The base of the body need to be broad.
  2. The Centre of gravity should be as low as possible.
  3. The vertical line through the center of gravity should fall within the base.

Multiple choice physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

Which of the following are the advantages of having low centre of gravity?

  1. It can corner at high speed,

  2. Much less risk of toppling over.

  3. It requires enough turning force to tip you over.

  4. None of the above
Reveal answer Fill a bubble to check yourself
A,B Correct answer
Explanation
1) Having low center of gravity can make a person more stable and thus has a less risk of toppling over and thus makes harder to knock them out.
2) And since the person having low center of gravity is more stable he can also corner very high speed over short distances.
Multiple choice physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

If linear density of a rod of length 3 m varies as  $\lambda=2+x$, then the position of the centre of gravity of the rod is 

  1. $\dfrac{7}{3}m$

  2. $\dfrac{12}{7}m$

  3. $\dfrac{10}{7}m$

  4. $\dfrac{9}{7}m$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The center of mass x_cm is calculated by the integral of (x * lambda * dx) / integral of (lambda * dx) from 0 to L. With lambda = 2 + x and L = 3, the numerator is integral from 0 to 3 of (2x + x^2) dx = [x^2 + x^3/3] from 0 to 3 = 9 + 9 = 18. The denominator is integral from 0 to 3 of (2 + x) dx = [2x + x^2/2] from 0 to 3 = 6 + 4.5 = 10.5. Thus, x_cm = 18 / 10.5 = 180 / 105 = 12 / 7.

Multiple choice physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

A bullet of mass 0.01$\mathrm { kg }$ and traveling at a speed of 500$\mathrm { m } / \mathrm { sec }$ strikes a block of which suspended by a string of length 5$\mathrm { m }$ . The centre of gravity of the block is found to vertical distance of 0.1$\mathrm { m }$ . What is the speed of the bullet after it emerges from the block?

  1. 359$\mathrm { m } / \mathrm { s }$

  2. 220$\mathrm { m } / \mathrm { s }$

  3. 204$\mathrm { m } / \mathrm { s }$

  4. 284$\mathrm { m } / \mathrm { s }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

By energy conservation of the suspended block we can say 

initial $KE=$ final potential energy
$\dfrac{1}{2}m{v^2} = mgH$
$\dfrac{1}{2}m{v^2} = gH$
$v = \sqrt {2gH} $
$v = \sqrt {2 \times 10 \times 0.1}  = 1.41\,m/s$
now$,$ by momentum conservation 
${P _{bullet}} = {P _{block}} + {P _{bullet}}$
$0.01 \times 500 = 1 \times 1.41 + 0.01 \times {v _f}$
$5 - 1.41 = 0.01 \times {v _f}$
$0.01{v _f} = 3.59$
${v _f} = 359\,m/s$
Hence,
option $(A)$ is correct answer.

Multiple choice physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

A metallic rod falls under gravity with its ends pointing east and west. Then

  1. an emf is induced in it as it cuts the magnetic lines of force

  2. no emf is induced at all

  3. two emf of equal nut opposite signs are induced, giving no emf is

  4. its acceleration is equal to the product of g and the radius of the rod.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When rod falls due to earth magnetic field an emf is induced 

Hence,
option $A$ is correct answer.

Multiple choice physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

The apparent weight of a person of mass m in an elevator is 2mg. The elevator is moving

  1. up with an acceleration of $\frac{g}{2}$

  2. up with an acceleration of g

  3. up with an acceleration of 2g

  4. down with an acceleration of g
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The apparent weight is given by N = m(g + a) for upward acceleration. If N = 2mg, then m(g + a) = 2mg, which simplifies to g + a = 2g, so a = g. The elevator is moving upward with an acceleration of g.

Multiple choice physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

A body of mass 5 kg initially moving with speed 10 m/s along x-axis in gravity free space explodes and breaks into three pieces of masses 1 kg, 1 kg and 3 kg. the two pieces of equal masses fly off with the same speed 20 m/s along y-axis and z-axis respectively. what is the velocity of heavier fragment?

  1. $ ( \frac {10}{3} \hat i - \frac {20}{3} \hat j - \frac {40}{3} \hat k ) m/s $

  2. $ ( \frac {50}{3} \hat i - \frac {20}{3} \hat j - \frac {20}{3} \hat k ) m/s $

  3. $ ( \frac {20}{3} \hat i - \frac {20}{3} \hat j - \frac {20}{3} \hat k ) m/s $

  4. None
Reveal answer Fill a bubble to check yourself
A Correct answer