Test: Unit & Measurement - UPSC MCQ

The statement describes the concept of inertia, which is an inherent property of matter. The mass of a body determines its resistance to changes in motion and is measured by the amount of inertia it possesses. The ratio of the force acting on an object to the acceleration it produces is known as its mass of inertia or simply inertia. This concept is fundamental to Newton's second law of motion, which states that the force acting on an object is directly proportional to its mass and the acceleration it experiences. Gravitational mass, the mass of the electromagnetic field, and the mass of internal organs are not relevant to the given statement.

To determine the mass of a body, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a), or F = ma.

Given: Force (F) = 90 N Acceleration (a) = 2.6 m/s²

Using the formula F = ma, we can rearrange it to solve for mass: m = F / a

Substituting the given values: m = 90 N / 2.6 m/s² ≈ 34.6 kg

Therefore, the mass of the body is approximately 34.6 kg.

The correct answer is b) 34.6 kg.

To calculate the acceleration of the automobile, we need to convert the speeds from km/h to m/s and use the formula for acceleration, which is given by:

Acceleration (a) = (final velocity - initial velocity) / time

Given: Initial velocity (u) = 18 km/h Final velocity (v) = 36 km/h Time (t) = 5 seconds

Converting the velocities to m/s: Initial velocity (u) = 18 km/h = 18 * (1000 m / 3600 s) = 5 m/s Final velocity (v) = 36 km/h = 36 * (1000 m / 3600 s) = 10 m/s

Using the formula for acceleration: Acceleration (a) = (10 m/s - 5 m/s) / 5 s = 5 m/s / 5 s = 1 m/s²

Therefore, the acceleration of the automobile is 1 m/s².

The correct answer is c) 1 m/s².

When a force is applied to move a block of wood on a flat surface, the frictional force develops in the direction opposite to the applied force. This frictional force is known as the static frictional force, which acts to oppose the motion or tendency of motion between the block and the surface.

The normal force (a force perpendicular to the surface) acts upwards to balance the weight of the block. The frictional force acts in the opposite direction of the applied force to prevent the block from sliding freely and to provide the necessary force to move the block.

Therefore, the correct answer is d) opposite to the applied force's direction.

Every body continues to be in its state of rest or of non-uniform motion in a straight line unless compelled by some external force to act otherwise. This is stated by: Newton's 1st law.

The components required to calculate the momentum of a body are velocity and mass. Momentum is defined as the product of an object's mass and its velocity. Mathematically, momentum (p) is given by:

p = m * v

Where: p = momentum m = mass of the body v = velocity of the body

Mass represents the amount of matter in an object, while velocity refers to the speed and direction of its motion. By multiplying the mass by the velocity, we can determine the momentum of the body.

Therefore, the correct answer is b) Velocity and mass.

When a passenger on a bus traveling at a constant speed is pushed backward, the bus accelerates forward due to an external force. This force is referred to as a fictitious or pseudo force.

Fictitious or pseudo forces are forces that appear to act on objects in non-inertial frames of reference, such as accelerating or rotating frames. In this case, when the passenger is pushed backward, their inertia tends to keep them at rest or in uniform motion. However, because the bus is accelerating forward, a fictitious force is experienced by the passenger, pushing them backward.

This force is not a real force in the sense that it does not arise from a physical interaction between objects. It is a result of the frame of reference being non-inertial, and it is necessary to explain the observed motion within that frame.

Inertia is the resistance of an object to changes in its state of motion. It depends on the mass of the object. Generally, objects with greater mass have greater inertia.

Comparing the given options:

a) A single atom: Atoms are extremely small and have very low mass compared to other objects. Therefore, a single atom has the lowest inertia among the given options.

b) A molecule: Molecules consist of multiple atoms bonded together. The mass of a molecule depends on the types and number of atoms it contains. It can vary significantly, but generally, molecules have more mass than a single atom. Therefore, a molecule has greater inertia compared to a single atom.

c) A one-rupee coin: A one-rupee coin typically has a mass greater than that of a molecule. It is composed of metal and has a significant size compared to atoms or molecules. Thus, a one-rupee coin has greater inertia than both a single atom and a molecule.

d) A cricket ball: A cricket ball is much larger and heavier than a one-rupee coin. It has a mass greater than all the previous options. Consequently, a cricket ball has the greatest inertia among the given options.

Therefore, the cricket ball (option d) has the greatest inertia.

The ratio of accelerations will be calculated as:

The correct answer is:

c) Moving with retardation.

Here’s why:

- If the pendulum's string points towards the front of the train, it suggests that the train is slowing down (decelerating or undergoing retardation). This happens because, due to inertia, the pendulum tends to keep moving forward even when the train is slowing down. As a result, the string appears to tilt towards the front of the train.

- If the train were accelerating, the pendulum would swing backward relative to the train, and its string would point toward the rear of the train.

Thus, the string pointing towards the front indicates that the train is moving with retardation  (deceleration).