Physics Test-25

Radius of \(n ^{\text {th }}\) orbit \(= a _0 n ^2\)

Radius of 1st orbit \(=a_0\)

Area of \(n ^{\text {th }}\) orbit \(=\pi a _0{ }^2 n ^4= A _{ n }\)

Area of 1st orbit \(=\pi a_0^2 A _1\)

\(\frac{ A _{ n }}{ A _1}= n ^4\) [T aking log both sides \(]\)

\(\Rightarrow \log \left(\frac{A_n}{A_1}\right)=4 \log n\).

Slope \(=4\), Linear graph.

As the truck is moving forward with a constant velocity, the tank along with the water is also moving under constant velocity. When a sudden brake is applied, it tends to oppose the forward motion of water in the tank. Due to the inertia of water, it would have a tendency to continue its forward motion. Therefore on sudden braking, it suddenly moves forward.

​Inertia is the property of an object by virtue of which it opposes any event that attempts to put the object in motion or to change its velocity. Therefore, an object at rest would want to continue staying at rest and an object in motion would have a tendency to continue its motion. Greater the mass of the object more will be the tendency to resist the events. 

Newton's first law of motion states that an object at rest remains at rest, or if in motion, remains in motion at a constant velocity unless acted on by a net external force. This law is also known as the law of inertia.

The above principle is related to Newton's second law of motion.

A cricket player extends his hands backwards while catching so that the ball takes longer to stop, thus reducing the chances of injury.

The longer it takes to stop the ball, the less the impact of the ball on the hands and thus the less chance of injury and injury from the ball.

An electric current can produceheating, chemical and magneticeffects

• Electric current is defined as the rate of flow of electrons through a conductor.
• Its SI unit is the ampere.
• An ampere is the flow of 1-coulomb charge per unit time through a conductor.
• There are a variety of effects produced by an electric current depending on the material through which it flows.
• Electric current is capable of producing heat, chemical and magnetic effects.
• If an electric current flows through a bulb, its filament heats up and glows.
• From this case, we can say that electric current has a heating effect.
• If an electric current is passed through a molten solution, as is done in electrolysis, a chemical change occurs which
• In this case, we can say that the electric current has a chemical effect.
• If a piece of metal is wound with a wire and an electric current is passed through the wire, the piece of metal acts as a magnet.
• This whole system is called a solenoid.

For work to be done, there should be a motion of the body in the direction of the force applied.

(A) The weight of a book at rest on a table cannot do any work as the book is at rest. So, the work done by this force is zero.
(B) The pulling force applied by the railway engine on its coaches is doing work, as the force applied by the engine results in the motion ofthe coaches.
(C) The tension force in an elastic band wrapped around a parcel cannot do any work, as there is no motion of the parcel because of thetension force of the rubber band.
(D) The push of a person’s feet on a floor when he is standing cannot do any work because there is no motion involved due to the appliedforce.

The resistance of a wire is calculated by,

\(R=\rho \frac{l}{A}\)

Where \(I\) is its length, \({A}\) area, and \(\rho\) is its metal resistivity.

• Here resistivity \(\rho\) depends on the material.
• So the resistance of a material depends on the length of the wire \(l\), Area of the wire \(A\), and property of the material.
• The resistance of the wire does not depend on the humidity of wire across the wire.

Given that,

\(\Rightarrow \vec{F}=6 \hat{i}-8 \hat{j}+10 \hat{k}\)

Resultant of force is given by

\(\Rightarrow|\vec{F}|=\sqrt{6^{2}+(-8)^{2}+10^{2}}=10 \sqrt{2}\)

\(\Rightarrow m=\frac{|\vec{F}|}{a}=\frac{10 \sqrt{2}}{1}=10 \sqrt{2}\) kg

Normal to the wave front is\((1,1,1)\).

So, angle between normal and x-axis is angle between light ray and \(x\)-axis.

So, \((i+j+k) \cdot(i)=\sqrt{3}(1) \cos \theta\)

\(\cos \theta=\frac{1}{\sqrt{3}} \)

\(\theta=\cos ^{-1}(\frac{1 }{\sqrt{3}})\)

Convection is the process of heat transfer by the bulk movement of molecules within fluids such as gases and liquids. The initial heat transfer between the object and the fluid takes place through conduction, but the bulk heat transfer happens due to the motion of the fluid.