Tag: acceleration due to gravity

Questions Related to acceleration due to gravity

What is the center of mass of an object?

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

  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.

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Correct Option: A
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.

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

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

  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.

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Correct Option: C
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.

The stability of a flexible body depends on:

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

  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.

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Correct Option: D
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.

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

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

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Correct Option: A,B
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.

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 

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

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

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

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

  4. $\dfrac{9}{7}m$

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Correct Option: B

If R is radius of the planet and g is the acceleration due to gravity at its surface then the body will reach the centre of the planet in time 

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

  1. 2$\pi$$\sqrt\frac{R}{g}$

  2. $\pi$$\sqrt\frac{R}{g}$

  3. $\frac{\pi}{2}$$\sqrt\frac{R}{g}$

  4. $\sqrt\frac{2R}{g}$

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Correct Option: B

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?

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

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

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

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

  4. 284$\mathrm { m } / \mathrm { s }$

Show answer
Correct Option: A
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.

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

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

  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.

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Correct Option: A
Explanation:

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

Hence,
option $A$ is correct answer.

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

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

  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

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Correct Option: B

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?

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

  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

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Correct Option: A