1.163 Acceleration of rocket

Problem 1.163:A small test rocket launched from rest travels $14.4 \:m$ upward in $2.0 \:s$. Determine acceleration of the rocket. Solution: The rocket was initially at rest. Then it speeds upward and covers a distance of $14.4 \:m$ in $2.0 \:s$. We will assume that...

1.162 Acceleration and velocity vector in projectile motion

Problem 1.162: A projectile is fired into the air at an angle with the ground. It follows the parabolic path as shown in the diagram, landing on the right. Neglect air resistance. At any instant, the projectile has a velocity $\vec{v}$ and an acceleration $\vec{a}$  ....

4.101 Speed of car – Doppler effect

Problem 4.101: A policeman on duty detects a drop of $30\: \%$ in the pitch of the horn of a motor-car as it crosses him. Calculate the speed of car, if the velocity of sound is $330m/s$. Solution: How to solve this problem? First try to visualize….There is a car and...

1.161:Tension in strings connected to moving blocks

Problem 1.161:A system consists of three blocks of masses $m_1$, $m_2$ and $m_3$ connected by a string passing over a pulley $P$. The mass $m_1$ hangs freely and $m_2$ and $m_3$ are on a rough horizontal table $($the coefficient of friction = $\mu$$)$. The pulley is...

1.160: Acceleration of connected blocks

Problem 1.160:A system consists of three blocks of masses $m_1$, $m_2$ and $m_3$ connected by a string passing over a pulley $P$. The mass $m_1$ hangs freely and $m_2$ and $m_3$ are on a rough horizontal table $($the coefficient of friction = $\mu$$)$. The pulley is...

Problem 3.102 Heating a gas at constant volume

Problem 3.102:A cylinder of fixed capacity $44.8$ liters contains helium gas at standard temperature and pressure. What is the amount of heat needed to raise the temperature of the gas in the cylinder by $15\:^oC$. Take $R$ as $8.314\:Jmol^{-1}$ Solution: The gas is...

3.101 Adiabatic expansion

Problem 3.101: A cylinder with a movable piston contains $3$ moles of hydrogen at standard temperature and pressure. The walls of the cylinder are made of a heat insulator, and the piston is insulated by having a pile of sand on it. By what factor does the pressure of...

6.100 refractive index of this material

Problem 6.100:The speed of light in a certain material is 50% of its speed in vacuum. What is the refractive index of this material? Solution: Refractive index of a material is defined as the ratio of speed of light in vacuum to the speed of light in that material....

1.159 Work done in uniform circular motion

Problem 1.159:.A body of mass $‘m’$ is moving in a circle of radius with a constant speed $‘v’$. Calculate the work done by the resultant force in moving the body over half circumference and full circumference respectively. Solution: This is motion along a circular...

6.99 Effective focal length of thin lenses in contact

6.99: A bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. Refractive index $n$ of the first lens is $1.5$ and that of the second lens is $1.2$. Both the curved surface are of the same radius of curvature $R \:=\: 14\:cm$. Find the...

5.154 Charge of elementary particles

Problem 5.154:What is the charge of $(i)$ electron $(ii)$ proton and $(iii)$ neutron? Solution: Charge of $(i)$ electron$ = - \:1.6 \times 10^{-19}\:C$                            $(ii)$ Proton$ = + \:1.6 \times 10^{-19}\:C$                            $(iii)$ Neutron=...

6.98 Time taken by light

Problem 6.98:A light ray is incident from air into a glass slab as shown in the diagram. Calculate the time spend by light ray inside glass. Refractive index of glass is $\sqrt{3}$. Solution: Here the ray is making angle of $30^o$ with the plane of the slab. Angle of...

6.97 Law of reflection.

Problem 6.97:A ray of light initially travelling horizontally,  is incident on the reflecting surface of a hemispherical object and gets deflected vertically upward as shown in the diagram. Find the value of height, $H$ at which the ray hit the object. Solution: The...

6.96 Angle of incidence

Problem 6.96: A ray is incident on a transparent  slab of refractive index $\sqrt{3}$.   The reflected and the refracted rays are mutually perpendicular.  Find the  angle of incidence. Solution: With reference to the diagram, $AO$ is the incident ray that makes angle...

6.95 Refractive index of a medium

Problem 6.95:Speed of light in a medium is one-third of the speed of light in vacuum. Determine the refractive index of the medium Solution: By definition refractive index $(n)$ of a medium is the ratio of speed of light in vacuum $(c)$to speed of light in that medium...

6.94 Angle of deviation in refraction

Problem 6.94: A plane separates a transparent media of refractive index of $\sqrt{3}$ from air. A ray of light coming from air is incident at an angle of $60^o$. Determine the angle of deviation of the ray. Solution: The light ray gets refracted as it enters the...

6.93 Focal length of a convex lens

Problem 6.93: A lens is made of glass having an index of refraction of $1.5$. Sides  of the lens are convex with a radius of curvature of $20 \:cm$. $(a)$ Find the focal length of the lens.  Solution: For a thin lens we have the relation...

6.92 Refraction at spherical surface

Problem 6.92: A point sized  object is buried in a spherical glass pebble of diameter $6.0\:cm$. The object appears at a depth of $2.0\:cm$ when viewed normal to the surface of the pebble. Find out how deep it actually is. Glass has refractive index of $1.5$....