A convex lens has a focal length of
Question: A convex lens has a focal length of $10 \mathrm{~cm}$. Find the location and nature of the image if a point object is placed on the principal axis at a distance of (a) $9.8 \mathrm{~cm}$, (b) $10.2 \mathrm{~cm}$ from the lens. Solution: And magnification $\mathrm{m}=\mathrm{v} / \mathrm{u}=510 /-9.8=-52.04 \mathrm{~cm}$ As $m1$. Then, Image is real and inverted....
Read More →A thin lens made of a material of refractive index
Question: A thin lens made of a material of refractive index $\mu 2$ has a medium of refractive index $\mu 1$ on one side and a medium of refractive index $\mu 2$ on the other side. The lens is biconvex and the two radii of curvature have equal magnitude R. A beam of light travelling parallel to the principal axis is incident on the lens. Where will the image be formed if the beam is incident from (a) the medium $\mu 1$ (b) from the medium $\mu s$ ? Solution:...
Read More →Lenses are constructed by a material of refractive index
Question: Lenses are constructed by a material of refractive index $1.50$. The magnitude of the radii of curvature are $20 \mathrm{~cm}$ and $30 \mathrm{~cm}$. Find the focal length of the possible lenses with the above specification. Solution:...
Read More →The radii of curvature of a lens are
Question: The radii of curvature of a lens are $20 \mathrm{~cm}$ and $30 \mathrm{~cm}$. The material of the lens has a refractive index $1.6$. Find the focal length of the lens (a) if it is placed in air, and (b) If it is placed in water (refractive index = 1.33). $\mu \mathrm{w}$ lens refractive index $=\mu \mathrm{g}$ Solution:...
Read More →A double convex lens has focal length
Question: A double convex lens has focal length $25 \mathrm{~cm}$. The radius of curvature of one of the surface is double of the other. Find the radii, if the refractive index of the material of the lens is 1.5. Solution:...
Read More →The convex surface of a thin concave convex lens of glass of
Question: The convex surface of a thin concave convex lens of glass of refractive index $1.5$ has a radius of curvature $20 \mathrm{~cm}$ The concave surface has a radius of curvature $60 \mathrm{~cm}$. The convex side is silvered side and placed on a horizontal surface as shown in figure (a) Where should a pin be placed on the axis so that its image is formed at the same place? (b) If the concave part is filled with water (refractive index $=4 / 3$ ) Find the distance through which the pin shou...
Read More →A hemispherical portion of the radius of a solid glass
Question: A hemispherical portion of the radius of a solid glass $(\mu=1.5)$ of radius $r$ is silvered to make the inner side reflecting. An object is placed in the axis of the hemisphere at a distance $3 \mathrm{r}$ from the center of the sphere. The light from the object is refracted of the sphere. The light from the object is refracted at the unsilvered part, and then reflected from the object is refracted from the silvered part and again refracted at the unsilvered part. Locate the final ima...
Read More →Solve the problem if the paperweight is inverted
Question: Solve the problem if the paperweight is inverted at its place so that the spherical surface touches the paper. Solution:...
Read More →A paperweight in the form of a hemisphere of
Question: A paperweight in the form of a hemisphere of radius $3.0 \mathrm{~cm}$ is used to hold down a printed page. An observer looks at the page vertically through the paperweight. At what height above the page will height above the page will the printed letters near the center appear to the observer? Solution:...
Read More →One end of a cylindrical glass rod
Question: One end of a cylindrical glass rod $(\mu=1.5)$ of radius $1.0 \mathrm{~cm}$ is rounded in the shape of a hemisphere. The rod is immersed in water $(\mu=4 / 3)$ and an object is placed in the water along the axis of the rod at a distance of $8.0 \mathrm{~cm}$ from the rounded edge. Locate the image of the object. Solution:...
Read More →A narrow pencil of parallel light is incident normally
Question: A narrow pencil of parallel light is incident normally on a solid transparent sphere of radius $\mathrm{r}$. What should be the refractive index if the pencil is to be focused (a) at the surface of the sphere, (b) at the center of the sphere? Solution:...
Read More →A biconvex thick lens is constructed with glass
Question: A biconvex thick lens is constructed with glass $(\mu=1.50)$ Each of the surface has a radius of $10 \mathrm{~cm}$ and the thickness at the middle is $5 \mathrm{~cm}$. Locate the image of an object placed far away from the lens. Solution:...
Read More →A small object is embedded in a glass sphere
Question: A small object is embedded in a glass sphere $\mu=1.5$ of radius $5.0 \mathrm{~cm}$ at a distance $1.5 \mathrm{~cm}$ left to the center. Locate the image of the object as seen by an observer standing (a) to the left of the sphere and (b) to the right of the sphere. Solution:...
Read More →Figure shows a transparent hemisphere of
Question: Figure shows a transparent hemisphere of radius $3.0 \mathrm{~cm}$ made of a material of refractive index $2.0$ (a) A narrow beam of parallel rays is incident on the hemisphere as shown in the figure. Are the rays totally reflected at the plane surface? (b) Find the image formed by the refractive index at the first surface. (c) Find the image formed by the reflection or by the refraction at the plane surface. (d) Trace qualitatively the final rays as they come out the hemisphere. Solut...
Read More →A spherical surface of radius
Question: A spherical surface of radius $30 \mathrm{~cm}$ separates two transparent media A and B with refractive index $1.33$ and $1.48$ respectively. The medium $\mathrm{A}$ is on the convex side of the surface. Where should a point object be placed in medium A so that the paraxial rays become parallel after refractive at the surface? Solution:...
Read More →Locate the image by refractive index
Question: Locate the image by refractive index in the situation shown in figure Solution:...
Read More →A light ray, going through a prism with the angle of
Question: A light ray, going through a prism with the angle of prism $60^{\circ}$, is found to deviate by $30^{\circ}$. What limit on the refractive index can be put from these data? Solution:...
Read More →Find the angle of deviation suffered by the light ray shown
Question: Find the angle of deviation suffered by the light ray shown in fig The refractive index $\mu=1.5$ for the prism material. Solution:...
Read More →Solve the following :
Question: A body rotating at $20 \mathrm{rad} / \mathrm{s}$ is acted upon by a constant torque providing it a deceleration of $2 \mathrm{rad} / S^{2}$. At what time will the body have kinetic energy same as the initial value if the torque continues to act? Solution: $\omega_{0}=20 \frac{\mathrm{rad}}{\sec } ; \alpha=-\frac{2 \mathrm{rad}}{\mathrm{s}^{2}} ; \omega=0$ $\omega=\omega_{0}+\alpha t_{1}$ Now, wheel accelerates and when angular velocity becomes $20 \mathrm{rad} / \mathrm{sec}$ it will ...
Read More →Solve the following :
Question: A cylinder rotating at an angular speed of $50 \mathrm{rev} / \mathrm{s}$ is brought in contact with an identical stationary cylinder. Because of the kinetic friction, torques act on the two cylinders, accelerating the stationary one and decelerating the moving one. If the common magnitude of the acceleration and deceleration be one revolution per second square, how long will it take before the two cylinders have equal angular speed? Solution: Let after time 't' their angular velocity ...
Read More →Solve the following :
Question: A wheel of mass $10 \mathrm{~kg}$ and radius $20 \mathrm{~cm}$ is rotating at an angular speed of $100 \mathrm{rev} / \mathrm{min}$ when the motor is turned off. Neglecting the friction at the axle, calculate the force that must be applied tangentially to the wheel to bring it to rest in 10 revolutions. Solution: $\omega_{0}=100 \frac{r e v}{\min }=100 \times \frac{2 \pi}{60}$ $\omega_{0}=\frac{10 \pi}{3} \frac{\mathrm{rad}}{\sec }$ $\theta=10 \mathrm{rev}=20 \pi \mathrm{rad}$ $\omega=...
Read More →Solve the following :
Question: A wheel rotating at a speed of 600 rpm (revolutions per minute) about its axis is brought to rest by applying a constant torque for 10 seconds. Find the angular deceleration and the angular velocity 5 seconds after the application of the torque. Solution: $\omega_{0}=600 \mathrm{rpm}=\frac{600}{60} \frac{\mathrm{rev}}{\mathrm{sec}}$ $\omega_{0}=10 \frac{\mathrm{rev}}{\mathrm{sec}} ; \omega=0 ; t=10 \mathrm{sec}$ $\omega=\omega_{0}+\alpha t$ $\alpha=-1 \mathrm{rev} / \mathrm{sec}^{2}$ F...
Read More →Solve the following :
Question: Because of the friction between the water in oceans with the earth's surface, the rotational kinetic energy of the earth is continuously decreasing. If the earth's angular speed decreases by $0.0016$ rad/day in 100 years, find the average torque of the friction on the earth. Radius of the earth is 6400 $\mathrm{km}$ and its mass is $6.0 \times 10^{24} \mathrm{~kg}$. Solution: $\alpha=\frac{\Delta \omega}{t}$ $=\frac{0.0016}{(86400 \times 100 \times 365 \times 86400)}$ $\tau=I \alpha$ $...
Read More →Solve the following :
Question: A flywheel of moment of inertia $5.0 \mathrm{~kg}-_{-} \mathrm{m}^{2}$ is rotated at a speed of $60 \mathrm{rad} / \mathrm{s}$. Because of the friction at the axle, it comes to rest in $5.0$ minutes. Find (a) the average torque of the friction, (b) the total work done by the friction and (c) the angular momentum of the wheel 1 minute before its stops rotating. Solution: $\omega_{0}=60 \frac{\mathrm{rad}}{\mathrm{s}} ; \omega=0 ; t=5 \mathrm{~min}=300 \mathrm{sec}$ $\omega=\omega_{0}+\a...
Read More →Solve the following :
Question: Calculate the torque on the square plate of the previous problem if it rotates about a diagonal with the same angular acceleration. Solution: M.I. of square plate about its diagonal $$ \begin{aligned} \mathrm{I}=\frac{m a^{2}}{12} \\ \tau=I \alpha \\ =\frac{(0.12)(0.05)^{2}}{12}(0.2) \\ =0.5 \times 10^{-5} \mathrm{~N}-\mathrm{m} \end{aligned} $$...
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