We know that `log_(10)100000 = 5`
Show that you get the same answer by writing `100000 = 1000 xx 100` and then using the product rule. Verify the answer.

We know log_(2)32 = 5 . Show that we get the same answer by writing 32 as 64/2 and then using the product rule. Verify your answer .

We have log_(2)32 = 5 . Show that we get the same result by writing 32 = 2^(5) and then using power rules. Verify the answer.

Take a small stone. Hold it in your hand. We know that the force gravity due to the earth acts on each and every object. When we were holding the stone in our hand, the stone was experiencing this force, but it was balanced by a force that we were applying onn it in the opposite direction. As a result, the stone remained at rest. Once we release the stone from our hands the only force that acts onit is the gravitational force of the earth and the stone falls down under its influence. Whenever an object moves under the influence of the force of gravity alone, it is said to be falling freely. Thus the released stone is in a free fall. In free fall, the initial velocity of the object is zero and goes on increasing due to acceleration due to gravity of the earth. During free fall, the frictional force due to air opposes the motion of the object anda buoyant force also acts on the object. Thus, true free fall is posible only in vacuum. For a freely falling object, the velocity on reachign the earth and the time taken for it can be calculated by using Newton's eqwuations of motion. For free fall the initial velocity u=0 and the acceleration a=g . Thus, we can write the equations as v="gt",s=1/2"gt"^(2),v^(2)=2gs For calculating the motion of an object thrown upwards, acceleration is negative, i.e. in a direction opposite ot the velocity and is taken to be -g. The magnitude of g is the same but the velocity of the object decreases due to -ve acceleration. The moon and the artificial satellites are moving only under the influence of the gravitational field of the earth. Thus they are in free fall. Write kinematic equations used in free fall?

Take a small stone. Hold it in your hand. We know that the force gravity due to the earth acts on each and every object. When we were holding the stone in our hand, the stone was experiencing this force, but it was balanced by a force that we were applying on it in the opposite direction. As a result, the stone remained at rest. Once we release the stone from our hands the only force that acts on it is the gravitational force of the earth and the stone falls down under its influence. Whenever an object moves under the influence of the force of gravity alone, it is said to be falling freely. Thus the released stone is in a free fall. In free fall, the initial velocity of the object is zero and goes on increasing due to acceleration due to gravity of the earth. During free fall, the frictional force due to air opposes the motion of the object and a buoyant force also acts on the object. Thus, true free fall is possible only in vacuum. For a freely falling object, the velocity on reaching the earth and the time taken for it can be calculated by using Newton's equations of motion. For free fall the initial velocity u=0 and the acceleration a=g . Thus, we can write the equations as v="gt",s=1/2"gt"^(2),v^(2)=2gs For calculating the motion of an object thrown upwards, acceleration is negative, i.e. in a direction opposite to the velocity and is taken to be -g. The magnitude of g is the same but the velocity of the object decreases due to -ve acceleration. The moon and the artificial satellites are moving only under the influence of the gravitational field of the earth. Thus they are in free fall. Which force acts on the stone in free fall after you release it?

Take a small stone. Hold it in your hand. We know that the force gravity due to the earth acts on each and every object. When we were holding the stone in our hand, the stone was experiencing this force, but it was balanced by a force that we were applying onn it in the opposite direction. As a result, the stone remained at rest. Once we release the stone from our hands the only force that acts onit is the gravitational force of the earth and the stone falls down under its influence. Whenever an object moves under the influence of the force of gravity alone, it is said to be falling freely. Thus the released stone is in a free fall. In free fall, the initial velocity of the object is zero and goes on increasing due toi acceleration due to gravity of the earth. During free fall, the frictional force due to air opposes the motion of the object anda buoyant force also acts on the object. Thus, true free fall is posible only in vacuum. For a freely falling object, the velocity on reachign the earth and the time taken for it can be calculated by using Newton's eqwuations of motion. For free fall the initial velocity u=0 and the acceleration a=g . Thus, we can write the equations as v="gt",s=1/2"gt"^(2),v^(2)=2gs For calculating the motion of an object thrown upwards, acceleration is negative, i.e. in a direction opposite ot the velocity and is taken to be -g. The magnitude of g is the same but the velocity of the object decreases due to -ve acceleration. The moon and the artificial satellites are moving only under the influence of the gravitational field of the earth. Thus they are in free fall. Which force acts on the stone when held in the hand?

Take a small stone. Hold it in your hand. We know that the force gravity due to the earth acts on each and every object. When we were holding the stone in our hand, the stone was experiencing this force, but it was balanced by a force that we were applying onn it in the opposite direction. As a result, the stone remained at rest. Once we release the stone from our hands the only force that acts onit is the gravitational force of the earth and the stone falls down under its influence. Whenever an object moves under the influence of the force of gravity alone, it is said to be falling freely. Thus the released stone is in a free fall. In free fall, the initial velocity of the object is zero and goes on increasing due to acceleration due to gravity of the earth. During free fall, the frictional force due to air opposes the motion of the object anda buoyant force also acts on the object. Thus, true free fall is posible only in vacuum. For a freely falling object, the velocity on reachign the earth and the time taken for it can be calculated by using Newton's eqwuations of motion. For free fall the initial velocity u=0 and the acceleration a=g . Thus, we can write the equations as v="gt",s=1/2"gt"^(2),v^(2)=2gs For calculating the motion of an object thrown upwards, acceleration is negative, i.e. in a direction opposite ot the velocity and is taken to be -g. The magnitude of g is the same but the velocity of the object decreases due to -ve acceleration. The moon and the artificial satellites are moving only under the influence of the gravitational field of the earth. Thus they are in free fall. What is free fall?

Take a small stone. Hold it in your hand. We know that the force gravity due to the earth acts on each and every object. When we were holding the stone in our hand, the stone was experiencing this force, but it was balanced by a force that we were applying on it in the opposite direction. As a result, the stone remained at rest. Once we release the stone from our hands the only force that acts on it is the gravitational force of the earth and the stone falls down under its influence. Whenever an object moves under the influence of the force of gravity alone, it is said to be falling freely. Thus the released stone is in a free fall. In free fall, the initial velocity of the object is zero and goes on increasing due to acceleration due to gravity of the earth. During free fall, the frictional force due to air opposes the motion of the object and buoyant force also acts on the object. Thus, true free fall is possible only in vacuum. For a freely falling object, the velocity on reaching the earth and the time taken for it can be calculated by using Newton's equations of motion. For free fall the initial velocity u=0 and the acceleration a=g . Thus, we can write the equations as v="gt",s=1/2"gt"^(2),v^(2)=2gs For calculating the motion of an object thrown upwards, acceleration is negative, i.e. in a direction opposite to the velocity and is taken to be -g. The magnitude of g is the same but the velocity of the object decreases due to -ve acceleration. The moon and the artificial satellites are moving only under the influence of the gravitational field of the earth. Thus they are in free fall. What is the initial velocity and what is the effect of gravitational acceleration on the object in free fall?

A tyre manufactureing company produces tyres of cars and buses. Three machines A, B, C are to be used for the production of these typres. Machines A and C are available for operation atmost 11 hours, whereas B must be operated for atleast 6 hours a day. the time required for construction of one typre the three machines given in the following table. Comapy sells all the tyres and gets a profit of Rs. 100 Rs 150 on a tyre of a car and bus respectively. The company wants to know how many numbers of each item to be produced to maximise the profit. To formulate a linear programmining problem, (i) Write the objective function. (ii) Write all constraints.

Answer the following questions . a. The earth's magnetic field varies from point is space. Does it also change with time ? It so , on what time scate does it change appreciably ? b. The earth's core is known to contain iron. Yet geologists do not regard this as a source of the earth's magnetism why ? c. The charged currents in the outer conducting regions of the earth's core are thought to be responsible for earth's magnetism . What might be the ' battery ' (i.e., the source of energy) to sustain these currents ? d. The earth may have even reversed the direction of its field several times during its history of 4 to 5 billion years. How can geologists know about the earth's field in such distant past ? e. The earth's field departs from its dipole substantially at large distances (greater than about 30,000 km) what agencies may be responsible for this distortion ? f. Interstellar space has an extremely weak magnetic field of the order of 10^(-12) T, Can such a weak field be of any significant consequence ? Explain. [Note : Exercise 2 is meant mainly to arouse your curiosity . Answers to some question above are tentative or unknown . Brief answers wherever possible are given at the end . For details , you should consult a good text on geomagnetism.]

Two indentical balls, each having a charge of 2.00xx10^(-7) C and a mass of 100g , are suspended from a common point by two insulating strings each 50 cm long. The balls are held at a separation 5.0cm apart and then released. Find (a) the electric force on one of the charged balls (b) the components of the resultant force on it along and perpendicular to the string (c) the tension is the string (d) the acceleration of one of the balls. Answers are to be obtained just after the release.