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First Year Physics Measurements The period of simple pendulum is measured by a stopwatch. What type of errors are possible in the time period?


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The period of simple pendulum is measured by a stopwatch. What type of errors are possible in the time period?

Name several repetitive phenomenon occurring in nature which could serve as reasonable time standard.
Name several repetitive phenomenon occurring in nature which could serve as reasonable time standard.

Name several repetitive phenomenon occurring in nature which could serve as reasonable time standard.

EXAMPLE 1.6Find the dimensions and hence the SI units of coefficient of viscosity \eta in the relation of Stokes law for the drag force F for a spherical object of radius r moving with velocity v given as F=6 \pi \eta rv.
EXAMPLE 1.6Find the dimensions and hence the SI units of coefficient of viscosity  \eta  in the relation of Stokes law for the drag force  F  for a spherical object of radius  r  moving with velocity  v  given as  F=6 \pi \eta  rv.

EXAMPLE 1.6Find the dimensions and hence the SI units of coefficient of viscosity \eta in the relation of Stokes law for the drag force F for a spherical object of radius r moving with velocity v given as F=6 \pi \eta rv.

What are the dimensions and units of gravitational constant G in the formula?\[F=G \frac{\mathbf{m}_{1} \mathbf{m}_{2}}{\mathbf{r}^{2}}\]
What are the dimensions and units of gravitational constant  G  in the formula?\[F=G \frac{\mathbf{m}_{1} \mathbf{m}_{2}}{\mathbf{r}^{2}}\]

What are the dimensions and units of gravitational constant G in the formula?\[F=G \frac{\mathbf{m}_{1} \mathbf{m}_{2}}{\mathbf{r}^{2}}\]

(b) How many nanoseconds in 1 year?
(b) How many nanoseconds in 1 year?

(b) How many nanoseconds in 1 year?

Does dimensional analysis give any information on constant of proportionality that may appear in an algebraic expression? Explain.
Does dimensional analysis give any information on constant of proportionality that may appear in an algebraic expression? Explain.

Does dimensional analysis give any information on constant of proportionality that may appear in an algebraic expression? Explain.

EXAMPLE 1.4Check the correctness of the relation v=\sqrt{\frac{F \times l}{m}} where V is the speed of transverse wave on a stretched string of tension \mathrm{F} length l and mass \mathrm{m} .
EXAMPLE 1.4Check the correctness of the relation  v=\sqrt{\frac{F \times l}{m}}  where  V  is the speed of transverse wave on a stretched string of tension  \mathrm{F}  length  l  and mass  \mathrm{m} .

EXAMPLE 1.4Check the correctness of the relation v=\sqrt{\frac{F \times l}{m}} where V is the speed of transverse wave on a stretched string of tension \mathrm{F} length l and mass \mathrm{m} .

(c) How many years in 1 second?
(c) How many years in 1 second?

(c) How many years in 1 second?

Show that the famous "Einstein equation" E=m c^{2} is dimensionally consistent.
Show that the famous "Einstein equation"  E=m c^{2}  is dimensionally consistent.

Show that the famous "Einstein equation" E=m c^{2} is dimensionally consistent.

Why do we find it useful to have two units for the amount of substance the kilogram and the mole?
Why do we find it useful to have two units for the amount of substance the kilogram and the mole?

Why do we find it useful to have two units for the amount of substance the kilogram and the mole?

EXAMPLE 1.5Derive a relation for the time period of a simple pendulum (Fig. 1.2) using dimensionsal analysis. The various possible factors on which the time period T may depend are(i) Length of the pendulum (l) .(ii) Mass of the bob (\mathrm{m}) .(iii) Angle \theta which the thread makes with the vertical.(iv) Acceleration due to gravity (g).
EXAMPLE 1.5Derive a relation for the time period of a simple pendulum (Fig. 1.2) using dimensionsal analysis. The various possible factors on which the time period  T  may depend are(i) Length of the pendulum  (l) .(ii) Mass of the bob  (\mathrm{m}) .(iii) Angle  \theta  which the thread makes with the vertical.(iv) Acceleration due to gravity (g).

EXAMPLE 1.5Derive a relation for the time period of a simple pendulum (Fig. 1.2) using dimensionsal analysis. The various possible factors on which the time period T may depend are(i) Length of the pendulum (l) .(ii) Mass of the bob (\mathrm{m}) .(iii) Angle \theta which the thread makes with the vertical.(iv) Acceleration due to gravity (g).

The length and width of a rectangular plate are measured to be 15.3 \mathrm{~cm} and 12.80 \mathrm{~cm} respectively. Find the area of the plate.
The length and width of a rectangular plate are measured to be  15.3 \mathrm{~cm}  and  12.80 \mathrm{~cm}  respectively. Find the area of the plate.

The length and width of a rectangular plate are measured to be 15.3 \mathrm{~cm} and 12.80 \mathrm{~cm} respectively. Find the area of the plate.

Write the dimension of:(ii) Density
Write the dimension of:(ii) Density

Write the dimension of:(ii) Density

Write the dimension of:(i) Pressure
Write the dimension of:(i) Pressure

Write the dimension of:(i) Pressure

The speed V of sound waves through a medium may be assumed to depend on (a) the density \rho of the medium and (b) its modulus of elasticity E which is the ratio of stress to strain. Deduce by the method of dimensions the formula for the speed of sound.
The speed  V  of sound waves through a medium may be assumed to depend on (a) the density  \rho  of the medium and (b) its modulus of elasticity  E  which is the ratio of stress to strain. Deduce by the method of dimensions the formula for the speed of sound.

The speed V of sound waves through a medium may be assumed to depend on (a) the density \rho of the medium and (b) its modulus of elasticity E which is the ratio of stress to strain. Deduce by the method of dimensions the formula for the speed of sound.

The period of simple pendulum is measured by a stopwatch. What type of errors are possible in the time period?
The period of simple pendulum is measured by a stopwatch. What type of errors are possible in the time period?
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The period of simple pendulum is measured by a stopwatch. What type of errors are possible in the time period?

Show that the expression \mathrm{V}_{\mathrm{f}}=\mathrm{v}_{\mathrm{i}}+ at dimensionally correct where \mathrm{V}_{1} is the velocity at t=0 a is acceleration and V_{f} is the velocity at time t .
Show that the expression  \mathrm{V}_{\mathrm{f}}=\mathrm{v}_{\mathrm{i}}+  at dimensionally correct where  \mathrm{V}_{1}  is the velocity at  t=0   a  is acceleration and  V_{f}  is the velocity at time  t .

Show that the expression \mathrm{V}_{\mathrm{f}}=\mathrm{v}_{\mathrm{i}}+ at dimensionally correct where \mathrm{V}_{1} is the velocity at t=0 a is acceleration and V_{f} is the velocity at time t .

(a) How many seconds are there in 1 year?
(a) How many seconds are there in 1 year?

(a) How many seconds are there in 1 year?

The wavelength \lambda of a wave depends on the speed v of the wave and its frequency f .Knowing that [\lambda]=[L][v]=\left[L T^{-1}\right] and [f]=\left[T^{-1}\right] Decide which of the following is correct f=v \lambda or f=v / \lambda
The wavelength   \lambda   of a wave depends on the speed   v   of the wave and its frequency   f  .Knowing that  [\lambda]=[L][v]=\left[L T^{-1}\right]  and  [f]=\left[T^{-1}\right] Decide which of the following is correct  f=v \lambda   or   f=v / \lambda

The wavelength \lambda of a wave depends on the speed v of the wave and its frequency f .Knowing that [\lambda]=[L][v]=\left[L T^{-1}\right] and [f]=\left[T^{-1}\right] Decide which of the following is correct f=v \lambda or f=v / \lambda

A light year is the distance light travels in one year. How many metres are there in one light year? (Speed of light =3.0 \times 10^{8} \mathrm{~ms}^{-1} )
A light year is the distance light travels in one year. How many metres are there in one light year? (Speed of light  =3.0 \times 10^{8} \mathrm{~ms}^{-1}  )
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A light year is the distance light travels in one year. How many metres are there in one light year? (Speed of light =3.0 \times 10^{8} \mathrm{~ms}^{-1} )

Give draw backs to use the period of a pendulum as a time standard.
Give draw backs to use the period of a pendulum as a time standard.
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Give draw backs to use the period of a pendulum as a time standard.

Find the value of g and its uncertainty using T=2 \pi \sqrt{\frac{l}{g}} from the following measurements made during an experiment.Length of simple pendulum l=100 \mathrm{~cm} Time for 20 vibrations =\mathbf{4 0 . 2 \mathrm { s }} Length was measured by a metre scale of accuracy upto 1 \mathrm{~mm} and time by stop watch of accuracy upto 0.1 \mathrm{~s} .
Find the value of   g   and its uncertainty using  T=2 \pi \sqrt{\frac{l}{g}}  from the following measurements made during an experiment.Length of simple pendulum  l=100 \mathrm{~cm} Time for 20 vibrations  =\mathbf{4 0 . 2 \mathrm { s }} Length was measured by a metre scale of accuracy upto  1 \mathrm{~mm}  and time by stop watch of accuracy upto  0.1 \mathrm{~s} .
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Find the value of g and its uncertainty using T=2 \pi \sqrt{\frac{l}{g}} from the following measurements made during an experiment.Length of simple pendulum l=100 \mathrm{~cm} Time for 20 vibrations =\mathbf{4 0 . 2 \mathrm { s }} Length was measured by a metre scale of accuracy upto 1 \mathrm{~mm} and time by stop watch of accuracy upto 0.1 \mathrm{~s} .

5.32 . Add the following masses given in kg upto appropriate precision. 2.1890.08911.8 and
 5.32 . Add the following masses given in kg upto appropriate precision.  2.1890.08911.8  and
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5.32 . Add the following masses given in kg upto appropriate precision. 2.1890.08911.8 and

Suppose we are told that the acceleration of a particle moving in a circle of radius r with uniform speed v is proportional to some power of r say r^{n} and some power of v say \mathbf{v}^{\mathrm{m}} determine the powers of r and v ?
Suppose we are told that the acceleration of a particle moving in a circle of radius  r  with uniform speed  v  is proportional to some power of  r  say  r^{n}  and some power of  v  say  \mathbf{v}^{\mathrm{m}}  determine the powers of  r  and  v  ?
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Suppose we are told that the acceleration of a particle moving in a circle of radius r with uniform speed v is proportional to some power of r say r^{n} and some power of v say \mathbf{v}^{\mathrm{m}} determine the powers of r and v ?

An old saying is that "A chain is only as strong as its weakest link". What analogue statement can you make regarding experimental data used in computation?
An old saying is that "A chain is only as strong as its weakest link". What analogue statement can you make regarding experimental data used in computation?
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An old saying is that "A chain is only as strong as its weakest link". What analogue statement can you make regarding experimental data used in computation?

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