Laws Of Motion And Gravitation

(ii) is correct.

In case of (i), balanced forces lead to zero net force. So, there is no acceleration as F = ma. For (iii), the force acts only on charged bodies. In most everyday objects, there are no excess charges and they are neutral bodies. So electrostatic force causes no acceleration on uncharged bodies. For (ii), there is a net force, so there is acceleration.

By Newton’s second law, force is defined as the rate of change of momentum. So (iii) is correct. Displacement is the rate of change of position. Acceleration is the rate of change of velocity. Impulse measures the impact of a force, given by force multiplied by time.

Momentum is given by the product of mass and velocity. Since the body is at rest, velocity is zero. Hence, momentum is zero.

W = mg,

where W is the weight,

m is the mass,

and g is acceleration due to gravity, which is 9.8 m/s².

So weight is equal to 50 kg × 9.8 m/s² = 490 N.

Liquid N₂ can achieve temperatures as low as -196 degrees C. It’s cryogenic. This allows preservation. Moreover, though liquid He is also cryogenic, it leads to formation of ice crystals which may damage the biotechnology products.

Let both have a mass of m.

Momentum of A = mass × velocity = 20m

Momentum of B = 50m

Force is defined as the rate of change of momentum. Since both A and B come to rest instantaneously, B exerts a greater force because it has greater momentum.

The velocity will still be 20 m/s. The force acts perpendicular to the velocity hence it has no component in the direction of motion and thus has no effect on the motion.

In big cities, it is difficult to set up overhead cables. So power cables are placed underground. But underground cables get heated up and this leads to power loss as well as rise in resistance of wires due to such temperature rise which leads to further power loss. So liquefied cryogenic gases are sprayed on the cables to cool them and prevent wastage of power.

The earth is an oblate spheroid. This means that the radius is least near the poles and maximum near the equator. Since the acceleration due to gravity on the surface of the earth is inversely proportional to the square of the radius, g is maximum at the poles and minimum at the equator.

The acceleration due to gravity, g is given by

Where G is the universal gravitational constant (= 6.67 × 10^-11 Nm²kg^-2),

M is the mass of the Earth,

R is the radius.

If the radius is reduced to half, g’ becomes

According to Newton’s first law, objects tend to resist a change in their state of rest or state of motion. So whenever the brakes are applied, the car comes to rest but the purse tends to stay in its state of motion. So it resists the change and as a result, the purse keeps moving forward and so it falls on the floor in front of the passenger’s seat.

When the ball falls in the fielder’s hands, it has very high speed and as a result, very large momentum. If the ball loses its momentum very quickly, the force exerted on the fielder’s hands will be very large. This could cause grievous injury. So the fielder pulls his hands back to increase the time taken for the ball to come to a stop, so that the rate of change of momentum reduces, the force on the fielder’s hands also reduces and there’s no injury as such.

(iii) is not applicable. A spring balance measures the weight of an object, which may change slightly from one place to

another. But the mass never changes.

Chandrayaan-1, India's first mission to Moon, was launched successfully on October 22, 2008 from SDSC SHAR, Sriharikota.

The following organisations are not associated with Chandrayaan –I

(v)WHO-World Health Organisation

(vi)ONGC-Oil and Natural Gas Corporation

Momentum = mass × velocity.

Momentum = .

So

Momentum = mass × acceleration × time

= mass × velocity

Liquid helium. Maintaining a large magnetic field required in an MRI machine requires superconductivity which is achieved by cooling the wires to very low temperatures to reduce the resistance to almost zero. This cooling is done using a continuous supply of liquid He.

(i) One newton is the force that produces an acceleration of 1 ms^-2 in an object of 1 kilogram mass, not gram. This is by definition.

(ii)Action and reaction don’t act on the same body. If there are 2 bodies A and B, if A exerts a force(action) on B, B will exert an equal and opposite force(reaction) on A according to Newton’s third law.

Cryogenic fuels are liquefied gases which have to be stored at very low temperatures. These are used as fuels in rockets. Ordinary fuels can’t be used there because of the absence of an environment that supports combustion.

By convention, anticlockwise moment is taken as positive, and clockwise moments are negative.

According to the equations of motion,

v² – u² = 2as …eq(1)

where v is the final velocity

u is the initial velocity

a is the acceleration

s is the displacement

From eq (1)

Here u = 75 m/s

v = 0 m/s

s = 5 cm = 0.05 m

So

= -56250 ms^-2

Hence average resistive force = ma = 20 g × -56250 ms^-2

= 0.02 kg × -56250 ms^-2

= -1125 N

Since F = ma,

where F is force,

m is mass and,

a is acceleration,

so, F = ma

= 65 kg × 0.3 ms^-2

= 19.5 N.

A spanner works on the principle of moment.

The diagram is shown below:

It is most effective when a small force creates a large moment. For this to happen, the perpendicular distance between the point of application and point of action of the force, r(in this case, the length of the handle) must be increased, since moment of a force ‘F’ = r × F. That’s why a spanner has a long handle.

When the boxer gets hit, the impact of the force of the punch is reduced if the time of impact is increased. That’s why the boxer always move along the direction of the punch of the opponent, to reduce the impact and thus reduce the chances of injury.

If rigid materials are used, a person falling on the mats will suffer great injury. While exercising or engaging in any sports activity, the person is having a considerable momentum. If s/he falls or slips, the momentum reduces to zero. The force exerted on the person’s body will depend on the rate of change of momentum, i.e. the time taken to come to rest. This time is large when the mats are soft (the force is small), and small when the mats are made of rigid material (the force is large).

The first principle involved in rocket propulsion is the Newton’s third law of motion: every action has an equal and opposite reaction. The second is the law of conservation of mass.

Moment is given by r × F.

Here F = mg

where g is the acceleration due to gravity,

m is mass.

So moment = 1.2 × mg

= 1.2 × 10 × 9.8

= 117.6 Nm in the clockwise direction.

F = mg

Where g is the acceleration due to gravity, m is the mass

F = 1 kg×9.8 ms^-2 = 9.8 N

Where G is the universal gravitational constant (= 6.67 × 10^-11 Nm²kg^-2),

M is the mass of the earth,

R is the radius of the earth.

If the density is doubled, the mass gets doubled. So

=

= 2g

Mass of the earth, M = 6 × 10²⁴ kg

Radius of the earth, R = 6.38 x 10³ km = 6.38 × 10³ × 10³ m

= 6.38 x 10⁶ m

Where G is the universal gravitational constant ( = 6.67 × 10^-11 Nm²kg^-2),

M is the mass of the Earth,

R is the radius.

So g =

= 0.9831 × 10

= 9.83 ms^-2

No, g is independent of her mass, so it will not change after she finishes her lunch though her mass has changed slightly.

Where G is the universal gravitational constant (= 6.67 × 10^-11 Nm²kg^-2),

M is the mass of the earth,

R is the radius of the earth.

M_asteroid = 104 kg

R_asteroid = 20 m

According to the law of conservation of momentum,

Initial momentum = Final momentum

Initial momentum = 0(because the system is initially at rest, velocity is zero)

0 = mv + MV (V is unknown)

V =

(i) 1:1. This is because the equations of motion are independent of the masses of the 2 balls. So they take equal amounts of time to reach the ground.

(ii) 2:1. We know F = ma. ’a’ in this case is the acceleration due to gravity, g. So force depends only on m, and here the masses are in 2:1 ratio.

(iii) 1:1. This is because the equations of motion are independent of the masses of the 2 balls.

(iv) 1:1. The acceleration due to gravity, g is independent of the masses of the 2 balls.

According to the equations of motion,

V² = u² + 2as

where v is the final velocity

u is the initial velocity

a is the acceleration

s is the displacement

Here acceleration is acceleration due to gravity,g.

So v = √(u² + 2gs)

= √(0 + 2×9.8×20)

= √196

= 14 m/s

Initial momentum = mv

Final momentum = -mv

Change in momentum = mv-(-mv) = 2mv = 2×1×14 = 28 kgms^-1

Where G is the universal gravitational constant( = 6.67 × 10^-11 Nm²kg^-2),

M is the mass of the earth,

R is the radius of the earth.

(given)

Now

= 9.8× (1/80) × 4²

= 1.96 ms^-2

To balance the seesaw, the weight moments on both sides should be balanced.

20×1.2 = 60×d

No, the horse exerts the reaction using its feet on the ground. It pushes the ground backwards and so the cart moves forward. The horse is just being lazy and stubborn!

Space Stations are used to study the effects of long-space flight on the human body since they provide zero gravity environments just like in outer space and there are adequate facilities for supporting human survival for long periods.

Newton’s law of gravitation states that the gravitational force between 2 objects is proportional to the product of the masses of the 2 objects and inversely proportional to the square of the distance between them.

Newton’s first law of motion states that objects tend to stay in their state of rest or state of motion. This property of an object is called inertia. So this law is often called the law of inertia. It gives us a qualitative idea about force as it tells us that force tends to change the state of motion of a body.

Acceleration of 10 kg mass =

Acceleration of 15 kg mass =

Where v is the final velocity,

u is the initial velocity,

t is the time taken.

Force on 15 kg mass,

F₁ = m₁a₁

= 15×2

= 30 N

Force on 10 kg mass,

F₂ = m₂a₂

= 10×(-3)

= -30 N

(i)a =

Where a is acceleration, F is force and m is mass.

(ii) According to the equations of motion,

T =

(iii) According to the equations of motion,

v = u + at

Where v is the final velocity,

u is the initial velocity,

a is the acceleration,

t is the time taken.

v = u + at

= 2×3 + 0 = 6 m/s

The law of conservation of momentum states that there is no change in momentum in an isolated system.

(i)Total momentum = mass × velocity = 10⁸×60×4 = 2.4×10¹⁰kgm/s

(ii)According to the law of conservation of momentum, the earth will gain the same momentum in the opposite direction so that there is no change in the momentum of the system (total momentum remains zero).

So the recoil velocity of the Earth =

= 4 × 10^-15 m/s

This velocity is negligibly small. So there’s no observable effect.

Newton’s law of gravitation states that the gravitational force between 2 objects is proportional to the product of the masses of the 2 objects and inversely proportional to the square of the distance between them.

Now

Where G is the universal gravitational constant( = 6.67 × 10^-11 Nm²kg^-2),

M is the mass of the earth,

R is the radius of the earth.

(given)

So,

Let M = 3 kg(the mass of the bomb)

m₁ = 2 kg(mass of one of the pieces)

m₂ = 1 kg(mass of the other piece)

v =0 m/s
v₁ = 3 m/s

v₂ = ?

Initial momentum = 0(because the bomb was at rest)

According to, the law of conservation of linear momentum,

Initial momentum = final momentum

M × v = m_{1 ×} v₁ + m_{2 ×} v₂
3 × 0 = 2 × 3 + 1 × v₂

The figure of the question is given below:

It is given in the question that the rope is taut, it means the rope is very tight.

Hence, the force exerted will be the same when on both the sides of the rope. i.e. The force exerted by the rope on the other person will also be 20 N, according to Newton’s 3^rd law of motion.

Now, the acceleration of the 60 kg man

= 0.33 ms^-2

The acceleration of the 50 kg man

= 0.4 ms^-2