Mixed MCQs

The Correct answer is Uniform motion.

Key Points

• Motion​:
  • It is a phenomenon in which an object changes its position with respect to time.
  • All motions are relative to some frame of reference. 
  • There are two types of motion:
    • Uniform Motion
    • Non-uniform Motion
• Uniform motion:
  • If an object is traveling with uniform motion, it is moving in a straight line at a constant speed.
  • For example, An object falling at terminal velocity experiences the same air resistance as its weight.
  • Newton's first law can be used to explain the movement of objects traveling with uniform motion.
  • Newton's first law is a body that is at rest or moving at a uniform rate in a straight line will remain in that state until some force is applied to it.

​Additional Information

• Retarding motion: The Motion in which the speed of the body gradually decreases.
• Non-uniform motion: If a body covers unequal distances in equal intervals of time
• Non-linear Motion: Nonlinear motion is motion along a curved path; It is the combination of two components of motion' horizontal motion (without acceleration) vertical motion (under the acceleration of gravity).

The correct answer is Velocity, time, and acceleration.

The first equation of motion gives the relation between initial velocity, final velocity, acceleration, and time.

• First equation of motion is given as v = u + at
  • Where, v = final velocity
  • u = initial velocity
  • a = acceleration
  • t = time taken

• The first equation of motion gives the value of velocity acquired by the body at any particular point of time t.
• The second equation of motion is given as s = ut + ½at²
• It gives the value of distance (s) traveled by a body at a given time t.
• Third equation of motion is given as v² = u² + 2as
• This equation gives the velocity of the body in traveling the distance s.

The correct answer is Displacement.

Key Points

•  Displacement
  • When a body moves from one position to another, the shortest distance between the initial position and final position of the body along with direction is known as Displacement.
  • Its SI unit is a meter.
  • It is a vector quantity.
  • Displacement of the object can be positive, negative, zero.
  • Displacement of the object can never be greater than the distance traveled by it.
• When there is no change in an initial position and final position even after covering some path, then it is considered zero displacements.

Additional Information

• Distance
  • It is the actual path covered by a moving body irrespective of the direction in which the body travels.
  • Its SI unit is a meter.
  • It is a scalar quantity.
  • An odometer is used to measure the distance traveled by the vehicle.  
• Speed
  • The time rate of change of position of the object in any direction is called the speed of the object.
  • It is a scalar quantity.
  • Its SI unit is m/s.
  • Speed= Distance travelled/Time taken
• Frequency
  • It tells us how frequently an event occurs.
  • The number of complete waves produced in one second is called the frequency of the waves.
  • Hertz is the SI unit of Frequency. It is named in the honor of Rudolf Hertz.
  • 1 Hertz= 1 vibration per second.

The correct answer is Its momentum is doubled.

Key Points

• Momentum is a vector quantity; it has both magnitude and direction.
• Isaac Newton’s second law of motion states that the time rate of change of momentum is equal to the force acting on the particle.
• Momentum can be calculated by multiplying the mass of an object by its forward velocity. (mv = kg*m/s).
• Mass and velocity are both directly proportional to the Momentum.
  • If you increase either mass or velocity, the Momentum of the object increases proportionally.
  • If you double the mass or velocity, you double the Momentum.
  • If you halve the mass or velocity, you half the Momentum.
• Newton's laws of motion-
  • ​Newton’s first law states that if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by force. This postulate is known as the law of inertia.
  • Newton’s second law is a quantitative description of the changes that a force can produce in a body's motion. It states that the time rate of change of a body's momentum is equal in both magnitude and direction to the force imposed on it. The momentum of a body is equal to the product of its mass and its velocity.
  • Newton’s third law states that when two bodies interact, they apply forces to one another equal in magnitude and opposite in direction. The third law is also known as the law of action and reaction. This law is important in analyzing static equilibrium problems, where all forces are balanced, but it also applies to bodies in uniform or accelerated motion.

Important Points

• Acceleration, the rate at which velocity changes with time in terms of both speed and direction. A point or an object moving in a straight line is accelerated if it speeds up or slows down. Motion on a circle is accelerated even if the speed is constant because the direction is continually changing.
• Kinetic energy, a form of energy that an object or a particle has because of its motion. If work, which transfers energy, is done on an object by applying a net force, the object speeds up and gains kinetic energy. Kinetic energy is a property of a moving object or particle and depends not only on its motion but also on its mass.
• Potential energy, stored energy that depends upon the relative position of various parts of a system. Spring has more potential energy when it is compressed than stretched. A steel ball has more potential energy raised above the ground than it has after falling to Earth.

The correct answer is 2 ms^-2

• We know that according to Newton's 2^nd law, 
  • ​Force = Mass × Acceleration
  • or \((\vec F = m \times \vec a)\)
• Here, F = 100 N and Mass = 50 Kg
• So, 100 = 50x a ⇒ a = 100/50 = 2.
• Hence, the acceleration will be 2 ms^-2.

• Force: A force is something that changes the state of rest or motion of a body.
  • It causes the body to start moving if it is at rest or stops if it is in motion or deflects from the initial path.
  • Force is a vector quantity having SI unit Newton (N) and dimension (MLT^-2).
• According to Newton’s Second law of motion
  • The rate of change of momentum of a body is directly proportional to the resulting force acting on a body
  • Mathematically it can be expressed as 
• \(\vec F \propto \frac{{d\vec p}}{{dt}}\;or\;\vec F = m \times a\)

The correct answer is 240 J.

Key Points

• When a force is applied to an object which causes displacement along the direction of force then the work is said to be done by that force.
• The work done by a force is defined as "the product of the component of the applied force on the block in the direction of the displacement and the magnitude of this displacement" is called work done.

Additional Information

• i.e., \(W = \vec F.d\vec x = Fdx\cos \theta \)

or in terms of magnitude, it can be given as

\(W\; = \;F \times s\)

• Here both force and displacement will be along the same direction since force is causing this displacement thus Work done is a scalar quantity.
  • Here,
  • Force applied on object = F
  • Displacement of object = dx
  • Distance traveled by an object = s
  • The angle between Force and displacement = θ
• Calculation:
  • Given that,
  • Person raised the box of weight 120 N through the height of 2 m
  • i.e., F = 120 N 
  • x = 2 m
• Thus from the above explanation, we can see that
• Work = Force × Distance moved in the direction of the force
• Force of 120 N is acting downwards, Therefore
  • Work Done = 120 × 2 = 240 J

CONCEPT:

• Power: The rate of work done is called power.
  • It is denoted by P.
  • Mathematically it is written as

\(Power\;\left( P \right) = \frac{{\;W}}{{t}}\)

CALCULATION:

Given - mass of 1^st person (m₁) = 80 kg, mass of 2^nd person (m2) = 60 kg, time (t₁) = 12 sec, and time (t2) = 11 sec​

• The power to take an object to a certain height in 12 sec by 1^st person is 

\(\Rightarrow P_1 = \frac{mgh}{t}=\frac{80gh}{12}\)       ----(1)

• The power to take an object to a certain height in 11 sec by 2^nd person is 

\(\Rightarrow P_1 = \frac{mgh}{t}=\frac{60gh}{11}\)       ----(2)

On dividing equations 1 and 2, we get

\(\Rightarrow \frac{P_1}{P_2} =\frac{\frac{80gh}{12}}{\frac{60gh}{11}}=\frac{11}{9}\)

Concept:

• Potential Energy: The energy of an object obtained by doing work against the conservative forces like spring force and gravitational force is called potential energy.
• The Gravitational potential energy of an object at a height h from the ground is given as

P = mgh

The spring potential energy of spring when it is stretched x distance from its natural length is given as

 \(P = \frac{1}{2}kx^2\)

• Kinetic Energy: The energy obtained by an object by virtue of its motion is called kinetic energy.

\(K = \frac{1}{2}mv^2\)

K is kinetic energy, v is the speed of the object, m is the mass of the object.

• Mechanical Energy: The sum of potential energy and kinetic energy is called mechanical energy.

Explanation:

So, from the above concept, it is clear that total mechanical energy is the sum of potential energy and kinetic energy. 

So, the answer is the Sum of Kinetic Energy and Potential Energy.

The correct answer is option 4) i.e. kg-1 m2

CONCEPT:

• Gravitational constant, G: G is a physical constant and therefore is universal in nature and has a constant value everywhere.
  • The value of G does not change with respect to time or place and is equivalent to 6.674 × 10-11 N m2 kg-2
  • The SI unit of G is N m2 kg-2
• Acceleration due to gravity, g: It is the acceleration of a body due to the force exerted from the earth's gravity.
  • It has a constant value of 9.8 m/s² within the surface of Earth.
  • The SI unit of g is m s^-2

EXPLANATION:

The unit of G = N m2 kg-2 = (mass × acceleration)m2 kg-2 = (kg × m/s²)m2 kg-2     (∵ N is the SI unit of force)

The unit of g = m s^-2​

Ratio, \(\frac{G}{g} = \frac{m^3 kg^{-1 }s^{-2 }}{m s^{-2}} =\) kg-1 m2

• 9.8 m/s² is the value of acceleration due to the gravity of the surface of the Earth.
• The acceleration which is gained by an object because of the gravitational force is called acceleration due to gravity.
• Its SI unit is m/s²