Unit and Measurement Questions

A block is dragged on smooth plane with the help of a rope which moves with velocity v. The horizontal velocity of the block is :

A man is walking on a road with a velocity 3 km/hr. Suddenly rain starts falling. The velocity of rain is 10 km/hr in vertically downward direction. The relative velocity of the rain is -

A particle when thrown vertically upward, moves such that it passes from same height at t = 2s and t = 10s, then this height is :

The smallest division on the main scale of a Vernier callipers is 1 mm and 10 vernier divisions coincide with 9 main scale divisions. While measuring the diameter of a ring, the zero mark of the vernier scale lies between 5.0 cm and 5.1 cm the eighth

If velocity [V] time [T] and force [F] are chosen as the base quantities, the dimensions of the mass will be:

PARSEC is a unit of

Energy of a particle is 5 J. If unit of length and time are doubled and unit of mass is halved then numerical value of the energy in this new system will be 5n. Value of n is

The time period of oscillation of a body is given by , K represents the kinetic energy, m mass, g acceleration due to gravity and A is unknown. If , then what is the value of x + y + z?

A gas bubble, from an explosion under water, oscillates with a period proportional to PadbEc. Where P is the static pressure, d is the density and E is the total energy of the explosion. Find the value of a + b + c.

If P and Q have different non-zero dimensions, which of the following operation is possible?

A wave is represented by y = a sin(At − Bx + C) where A, B, C are constants and t is in seconds and x is in meter. The dimensions of A, B, C are

If the unit of length and force be increased four times, then the unit of energy is

(where v = velocity, F = force). Find the dimensions of α and β.

Velocity is a derived physical quantity which depends on ________ fundamental quantities.

The pressure of 106 dyne/cm2 is equivalent to

The physical quantity which has dimensional formula as that of Energy/(Mass × Length) is [Power = Energy/Time]

Considering force (F), velocity (v) and energy (E) as fundamental quantities, match the correct dimensions of following quantities. (Pressure = Force/Area, Light year → Distance travelled by light in one year)

When Bernoulli's theorem is expressed as = constant, the dimensions of the constant on the right hand side of the equation are given as (p → pressure = Force/Area, h → height, v → velocity, ρ → density = Mass/Volume, g → acceleration due to gravity)

Using the principle of homogeneity of dimensions find which is correct? [r → distance, T → time, G → Universal Gravitational Constant]

Force acting on a particle is given by F = (A − x)/Bt, where x is in metre and t is in seconds. The dimension of B is

Dimensional formula for energy in terms of momentum (p), area (A) and time (T) is. [Momentum = Mass × Velocity]

An unknown quantity α is expressed as where m = mass, a = acceleration, l = length. The unit of α should be

The period of oscillation of a simple pendulum in the experiment is recorded as 2.6s, 2.5s, 2.4s, 2.7s and 2.8s respectively. The average absolute error is

Let E represent energy, m mass, L angular momentum, G gravitational constant. Dimension of (E L²)/(m⁴ G²) is:

A wire has a mass (0.3 ± 0.003) g, radius (0.2 ± 0.002) cm and length (5 ± 0.05) cm. The maximum percentage error in the measurement of its density in g/cm³ is

The magnitude of the difference between the individual measured value and true value of the quantity is known as

A micrometer has 150 equal divisions on the circular scale, and on one full rotation of circular scale the main scale advances by 0.02 cm then the least count of the micrometer (in cm) is

The value of (24.36 + 0.0623 + 256.2) with proper significant digit is

If force is given by F = A + Bt², where x is displacement and t is time, then dimensions of is

Which of the following is derived unit?

If A and B are two different physical quantities, then which of the following operations must be invalid?

A Vector (where O is origin) is represented as = 3î + 3ĵ. If the vector is rotated by 45° in clockwise direction, the new vector is represented as

When nothing is placed between the jaws of a vernier calliper, the 9th division of vernier scale coincides with 6th division of main scale. If one main scale division is 0.01 mm, then the least count of instrument is

Assertion : Number of significant digit in 0.002 is one and that in 0.500 is three. Reason : If number is less than 1, then zeroes before the non-zero numbers are not significant and zeroes after non-zero number are significant.

SI unit of luminous intensity is

Two particles are projected at speed 3 m/s and 6 m/s horizontally in the same direction from the top of a tower. If both of them strike the ground at points 12 m apart, then the height of tower will be [Use g = 10 m/s²]

With regards to significant figures 4.000 × 10³ m can be written as

A bullet is fired horizontally aiming at an object which starts falling at the instant when the bullet is fired (as shown). Position ‘A’ is taken as origin and speed of bullet is 10 m/s. If the bullet hits the object after 1 second, then coordinates

A particle starts from rest on a circle of radius m with uniformly increasing speed. If it completes 5 revolutions in 5 seconds, then its tangential acceleration is

Linear mass density has dimensional formula as

Two quantities are measured as A = 1.0 m ± 0.2 m and B = 2.0 m ± 0.2 m. The correct value of should be reported as

A system of units has 10 kg, 10 cm and 10 s as the units of mass, length and time respectively. The value of 10 N in this system will be

Time period of a simple pendulum is recorded in three experiments as 1.9, 2.0 and 2.1, then

Choose the correct statement.

If velocity (V), mass (M) and time (T) are taken as fundamental quantities, then dimensional formula of Young’s Modulus is (Young’s modulus has same dimensions as pressure)

Number of significant figures in 0.004900 is

If dimensional formula of a physical quantity is [MaLbTc], then the physical quantity can be

If each division on the main scale is 1 mm, then which of the following vernier scales gives vernier constant equal to 0.05 mm?

Power of a force varies with displacement x and time t as , where a and b are dimensional constants, the dimensional formula of [ab] is

A quantity ‘x’ is given as . If percentage error in measurements of α, β, ρ and γ, are %, %, 2% and % respectively, then maximum percentage error in ‘x’ is