A voltmeter coil has resistance 50.0Ω and resistor of 1.15kΩ
Question: A voltmeter coil has resistance $50.0 \Omega$ and resistor of $1.15 \mathrm{k} \Omega$ is connected in series. It can read potential differences up to 12 volts. If this same coil is used to construct an ammeter which can measure currents up to $2.0 \mathrm{~A}$, what should be the resistance of the shunt used? Solution:...
Read More →An inverted cone has a depth of
Question: An inverted cone has a depth of $40 \mathrm{~cm}$ and a base of radius $5 \mathrm{~cm}$. Water is poured into it at a rate of $1.5$ cubic centimetres per minute. Find the rate at which the level of water in the cone is rising when the depth is $4 \mathrm{~cm}$. Solution:...
Read More →An ammeter is to be constructed which can read currents up to 2.0A.
Question: An ammeter is to be constructed which can read currents up to $2.0 \mathrm{~A}$. If the coil has a resistance of $25 \Omega$ and takes $1 \mathrm{~mA}$ for full-scale deflection, what should be the resistance of the shunt used? Solution:...
Read More →A 2-m tall man walks at a uniform speed of a uniform speed of
Question: A 2-m tall man walks at a uniform speed of a uniform speed of $5 \mathrm{~km}$ per hour away from a 6-metre-high lamp post. Find the rate at which the length of his shadow increases. Solution:...
Read More →A voltmeter consists of a 25Ω coil connected in series with a 575Ω resistor.
Question: A voltmeter consists of a $25 \Omega$ coil connected in series with a $575 \Omega$ resistor. The coil takes $10 \mathrm{~mA}$ for full scale deflection. What maximum potential difference can be measured on this voltmeter? Solution:...
Read More →The voltmeter shown in figure (32-E25) reads 18V across the 50Ω resistor.
Question: The voltmeter shown in figure (32-E25) reads $18 \mathrm{~V}$ across the $50 \Omega$ resistor. Find the resistance of the voltmeter. Solution:...
Read More →A stone is dropped into a quiet lake and waves move in circles at a speed of
Question: A stone is dropped into a quiet lake and waves move in circles at a speed of $3.5 \mathrm{~cm}$ per second. At the instant when the radius of the circular wave is $7.5 \mathrm{~cm}$. how fast is the enclosed area increasing? (Take $\pi=$ 22/7.) Solution:...
Read More →A voltmeter of resistance 400Ω is used to measure
Question: A voltmeter of resistance $400 \Omega$ is used to measure the potential difference across the $100 \Omega$ resistor in the circuit shown in figure (32-E24). (a) What will be the reading of voltmeter? (b) What was the potential difference across $100 \Omega$ before the voltmeter was connected? Solution:...
Read More →The bottom of a rectangular swimming tank is
Question: The bottom of a rectangular swimming tank is $25 \mathrm{~m}$ by $40 \mathrm{~m}$. Water is pumped into the tank at the rate of 500 cubic metres per minute. Find the rate at which the level of water in the tank is rising. Solution:...
Read More →A balloon which always remains spherical is being inflated by pumping in 900 cubic centimetres of gas per second.
Question: A balloon which always remains spherical is being inflated by pumping in 900 cubic centimetres of gas per second. Find the rate at which the radius of the balloon is increasing when the radius is $15 \mathrm{~cm}$. Solution:...
Read More →The emf ε and the internal resistance r of
Question: The emf $\varepsilon$ and the internal resistance r of the battery shown in figure (32-E23) are $4.3 \mathrm{~V}$ and $1.0 \Omega$ respectively. The external resistance $R$ is $50 \Omega$. The resistances of the ammeter and voltmeter are $2.0 \Omega$ and $200 \Omega$ respectively. (a) Find the readings of the two meters. (b) The switch is thrown to the other side. What will be the readings of the two meters now? Solution:...
Read More →The volume of a spherical balloon is increasing at the rate of 25 cubic centimetres per second.
Question: The volume of a spherical balloon is increasing at the rate of 25 cubic centimetres per second. Find the rate of change of its surface at the instant when its radius is $5 \mathrm{~cm}$. Solution:...
Read More →An infinite ladder is constructed with 1Ω and 2Ω resistors as
Question: An infinite ladder is constructed with $1 \Omega$ and $2 \Omega$ resistors as shown in figure (32-E22). (a) Find the effective resistance between the points $A$ and $B$. (b) Find the current that passes through the $2 \Omega$ resistor nearest to the battery. Solution:...
Read More →The radius of an air bubble is increasing at the rate of
Question: The radius of an air bubble is increasing at the rate of $0.5$ centimetre per second. At what rate is the volume of the bubble increasing when the radius is 1 centimetre? Solution:...
Read More →The radius of a circular soap bubble is increasing at the rate of
Question: The radius of a circular soap bubble is increasing at the rate of $0.2 \mathrm{~cm} / \mathrm{s}$. Find the rate of increase of its surface area when the radius is $7 \mathrm{~cm}$. Solution:...
Read More →Find the equivalent resistances of the networks
Question: Find the equivalent resistances of the networks shown in figure (32-E21) between the points a and b. Solution:...
Read More →The side of a square sheet of metal is increasing at 3 centimetres per minute.
Question: The side of a square sheet of metal is increasing at 3 centimetres per minute. At what rate is the area increasing when the side is $10 \mathrm{~cm}$ long? Solution:...
Read More →Twelve wires, each having equal resistance r,
Question: Twelve wires, each having equal resistance $r$, are joined to form a cube as shown in figure (32-E20). Find the equivalent resistance between the diagonally opposite points a and $f$. Solution:...
Read More →The radius of a circle is increasing uniformly at the rate of
Question: The radius of a circle is increasing uniformly at the rate of $0.3$ centimetre per second. At what rate is the area increasing when the radius is $10 \mathrm{~cm}$ ? (Take $\pi=3.14 .)$ Solution:...
Read More →Consider the circuits shown in (32-E19a).
Question: Consider the circuits shown in (32-E19a). Find (a) The current in the circuit, (b) The potential drop across the $5 \Omega$ resistor, (c) The potential drop across the $10 \Omega$ resistor. (d) Answer the parts (a), (b) and (c) with reference to figure (32-E19b). Solution:...
Read More →The radius of a circle is increasing at the rate of
Question: The radius of a circle is increasing at the rate of $0.7 \mathrm{~cm} / \mathrm{s}$. What is the rate of increase of its circumference? Solution:...
Read More →The side of a square is increasing at the rate of
Question: The side of a square is increasing at the rate of $0.2 \mathrm{~cm} / \mathrm{s}$. Find the rate of increase of the perimeter of the square. Solution:...
Read More →Find the current in the three resistors shown in figure (32-E15).
Question: Find the current in the three resistors shown in figure (32-E15). Solution:...
Read More →Find the current through the 10Ω resistor shown in figure (32-E14)
Question: Find the current through the $10 \Omega$ resistor shown in figure (32-E14) Solution:...
Read More →Solve the following :
Question: A Mars satellite moving in an orbit of radius $9.4 \times 103 \mathrm{k} \mathrm{m}$ takes $27540 \mathrm{~s}$ to complete one evolution. Calculate the mass of Mars. Solution: Time period of revolution of satellite around the mars is given by $\mathrm{T}=2 \pi \sqrt{\frac{r^{\mathrm{s}}}{G M}}$ $M=$ Mars mass $r=$ Distance of the satellite from center of the planet $27540=2 \times 3.14 \sqrt{\frac{\left(9.4 \times 10^{\mathrm{s}} \times 10^{\mathrm{s}}\right)^{\mathrm{s}}}{6.67 \times ...
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