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...

1.160: 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...

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 $1.5$....