The echo will be heard when the sound reaches back at the place of firing. So, the total distance travelled by sound is 2\(\times\)1.2 km = 2.4 km = 2400 m.
\(speed=\frac{2400m}{8s}=300\ ms^{-1}\)

Radius of the curve r = 36 m.
Coefficient of friction μ= 0.53
Acceleration due to gravity g = 10 ms^-2
vmax=\(\sqrt { \mu rg } =\sqrt { 0.53\times 36\times 10 } \)=13.81 ms^-1.

We know that a=\(\left[ \frac { F }{ { m }_{ 1 }+{ m }_{ 2 }+{ m }_{ 3 } } \right] =\frac { 50N }{ 10kg+7kg+2kg } =\frac { 50 }{ 19 } \)= 2.63 ms^-2

Maximum Range = 3.46 km
So it is not possible.

V = 21.8 kmh^-1
angle with north, \(\theta=23.4^0\)

Angle of inclination θ = 45⁰
∴ Coefficient of friction μ= tan θ = tan45⁰=1

F_cp = \(\frac { \frac { 1 }{ 4 } \times (2)^{ 2 } }{ 3 } \)=0.333N

(i) Linear motion,
(ii) Circular motion,
(iii) Rotational motion,
(iv) Vibratory motion.

The straw paper between the China ware increases the Time of experiencing the jerk during transportation. Hence impact of force reduces on China wares.

Yes, if the external forces acting on the body can be represented in magnitude and direction by the sides of a closed polygon taken in the same order.

Force of friction between the tyre and road provides centripetal force.

To reduce friction and so to reduce wear and tear.

No. (highest point of vertical upward motion under gravity).

Both during its upward and downward motion, the ball continues to move inertia of motion with the same horizontal velocity as the train. In this period, the ball covers the same horizontal distance as the train and so it comes back to the thrower's hand.

In terms of components, we can write
\(\vec a=\frac{dv_x}{dt}\hat i+\frac{dv_y}{dt}\hat j+\frac{dv_z}{dt}\hat k=\frac{d\vec v}{dt}\)
Thus \(a_x=\frac{dv_x}{dt},a_y=\frac{dv_y}{dt},a_z=\frac{dv_z}{dt}\) are the components of instantaneous acceleration.
Since each component of velocity is the derivative of the corresponding coordinate, we can express the components a_x, a_y, and a_z as
\(a_x=\frac{d^2x}{dt^2},a_y=\frac{d^2y}{dt^2},a_z=\frac{d^2z}{dt^2}\)
Then the acceleration vector \(\vec a\) itself is
\(\vec a=\frac{d^2x}{dt^2}\hat i+\frac{d^2y}{dt^2}\hat j+\frac{d^2z}{dt^2}\hat k=\frac{d^2\vec r}{dt^2}\)
Thus acceleration is the second derivative of position vector with respect to time.

4

Speed of light in vacuum, c = 1 new unit of length s^-1
t = 8 min. 20 sec, = 500 s
x = ct = 1 new unit of length s^-1\(\times\)500s
x= 500 new unit of length

The total distance the athlete covered = 3\(\times\)circumference of track
Distance = 3\(\times\) 2\(\pi\)\(\times\) 50 = 300\(\pi\) m (or)
Distance = 300\(\times\)3.14 = 942 m
The displacement is zero, since the athlete reaches the same point A after three rounds from where he started.

We can resolve all the vectors in x, y and z components with respect to Cartesian coordinate system.
Once we resolve the components we can separately equate the x components on both sides, y components on both sides, and z components on both the sides of the equation, we then get
\(F_{1x}+F_{2x}+F_{3x}=F_{4x}\)
\(F_{1y}+F_{2y}+F_{3y}=F_{4y}\)
\(F_{1z}+F_{2z}+F_{3z}=F_{4z}\)

Using the equation,
\(|\vec A-\vec B|=\sqrt{5^2+7^2-2\times 5\times 7\cos60^o}=\sqrt{25+49-35}=\sqrt{39}\) units
The angle that \(\vec A-\vec B\) makes with the vector \(\vec A\) is given by
\(\tan\alpha_2=\frac{7\sin60^o}{5-7\cos60^o}=\frac{7\sqrt{3}}{10-7}=\frac{7}{\sqrt{3}}\)= 4.041
\(\alpha_2=tan^{-1}(4.041)=76^o\)

101.6\(\times\)10⁶

three

five

one

Given: r = 100m, μ = 0.8, g=9.8 ms^-2
The car will not skid if the force of friction provides the necessary centripetal force.
∴ f = \(\mu mg=\frac { m{ v }_{ max }^{ 2 } }{ r } \)
or vmax = \(\sqrt { \mu rg } =\sqrt { 0.8\times 100\times 9.8 } \) = 28ms^-1

Yes, for example, a plane angle has no dimensions but has unit like radian for its measurement.

Since fmal and initial positions are same hence displacement of the boy will be, \(\triangle r=r-r=0\).

The digits that are known reliably plus the first uncertain digit are known as significant figures or significant digits.

For measurement of small masses of atomic/subatomic particles etc., we make use of a mass spectrograph.

The mean distance of the Earth from the Sun
1 AU = 1.496\(\times\)10¹¹m

No, because equations of motions are applicable as long as the acceleration is uniform.

Triple point of water is the temperature at which saturated vapour, pure and melting ice are all in equilibrium. The triple point temperature of water is 273.16K.

Horizontal component of the normal reaction of the road provides the necessary centripetal force for the vehicle to move it along the curved path.

Rolling friction < Sliding friction

Quantities that can be measured, and in terms of which laws of physics are described are called physical quantities. Examples are length, mass, time, force, energy, etc.

All psychological interactions can be derived from a physical process. The movements of neuro transmitters are governed by the physical properties of diffusion and molecular motion. The functioning of our brain is related to our underlying dualism.

If a very large force acts on an object for a very short duration, then the force is called impulsive force or impulsive.

In accelerated motion, if the change in velocity of an object per unit time is same (constant) then the object is said to be moving with uniformly accelerated motion.
On the other hand, if the change in velocity per unit time is different at different times, then the object is said to be moving with non-uniform accelerated motion.

No.

(i) Gravitational force (mg) acting downwards
(ii) Normal force (mg) acting upwards
(iii) Frictional force (F_s) acting horizontally Inwards along the road.

(i) Ball bearings provides another effective way to reduce the kinetic friction.
(ii) If ball bearings are fixed between two surfaces, during the relative motion only the rolling friction comes to effect and not kinetic friction.
(iii) The rolling friction is much smaller than kinetic friction; hence the machines are protected from wear and tear over the years.

(i) Second biker cannot apply Newton's second law, because he is moving with acceleration \(\overset { \rightarrow }{ a } \) with respect to Earth (he is not in inertial frame).
(ii) But the first biker can apply Newton's second law because he is moving at constant velocity with respect to Earth (he is in inertial frame).

The inability of an object to change its state of uniform speed (constant speed) on its own is called inertia of motion.

(i) Inertia of rest: When a stationary bus starts to move, the passengers experience a sudden backward push.
(ii) Due to inertia, the body (of a passenger) will try to continue in the state of rest, while the bus moves forward. This appears as a backward push.

Time delay T = 5.6s
\(t={{T}\over{2}}={{5.6}\over{2}}=2.8\)
Speed of radio waves = speed of light (v) 3\(\times\)10⁸ m/s
Distance from the surveillance ship to enemy ship D = v \(\times\) t
= 3\(\times\)10⁸\(\times\)2.8
= 8.4\(\times\)10⁸m
Distance (D) = 8.4\(\times\)10⁸ km.

Distance, D = 824.7\(\times\)10⁶ km
\(\theta=35.72"={{35.72}\over{60\times 60}}\times{{\pi}\over{180}}\) rad
\(\theta \ \rightarrow\) is angular diameter
Diameter, d = ?
\(d=D\times\theta\)
\(=824.7\times{10}^{6}\times{{35.72}\over{60\times 60}}\times{{\pi}\over{180}}\) km 
\(=824.7\times{10}^{6}\times{{35.72}\over{3600}}\times{{\pi}\over{180}}\) km
\(=824.7\times{10}^{6}\times{{35.72\times3.14}\over{3600\times180}}\)km
Diameter of Jupiter = 1.427\(\times\)10⁵ km

(i) Fractional error \(=\delta_t={{\triangle t}\over{t}}\)
\(={{0.01}\over{5}}=0.002.\)
(ii) Percentage error \(=\delta_t={{\triangle t}\over{ t}}\times100\%\)
= 0.002\(\times\)100%
= 0.02%

(i) Initial speed (u)
(ii) The sine of angle of projection (\(\theta\)).
(iii) It inversely depends on acceleration due to gravity 'g'.

\(|3\hat { i } -2\hat { j } +\sqrt { 3 } \hat { k } |=\sqrt { { 3 }^{ 2 }+{ 2 }^{ 2 }+{ \sqrt { 3 } }^{ 2 } } \)
\(\sqrt { 9+4+3 } =\sqrt { 16 } =4\)

The length of a vector is called magnitude of the vector. It is always a positive quantity. The magnitude or norm is denoted by \(\left| \overrightarrow { A } \right| \) .

If the x, y and z axes are drawn in anticlockwise direction then the coordinate system is called as "right-handed Cartesian coordinate system".

Technology is the application of the principles of physics for practical purposes. The application of knowledge for practical purposes in various fields to invent and produce useful products or to solve problems is known as technology

Scalar is a property which can be described only by magnitude.
Examples:
Distance, mass, temperature, speed and energy.

From the safe turn condition the speed of the vehicle (v) must be less than or equal to \(\sqrt { { \mu }_{ s }rg } \)
v ≤ \(\sqrt { { \mu }_{ s }rg } \)
\(\sqrt { { \mu }_{ s }rg } \)=\(\sqrt { 0.81\times 10\times 10 } \)=9 ms^-1
For car C, \(\sqrt { { \mu }_{ s }rg } \) is less than v.
The speed of car A, B and Care 7 m s^-1, 8 m s^-1 and 10 m s^-1 respectively. The cars A and B will have safe turns. But the car C has speed 10 m s^-1 while it turns which exceeds the safe turning speed. Hence, the car C will skid.

Circular wheels roll on the road and rolling friction comes into play during the motion of automobile.
Rolling friction is less than the sliding friction. It is due to this reason that wheels of automobiles are made circular.

Time becomes irrelevant. Because day and year based on spinning and revolution of the planet. So each planet has its own year length.
Eg: Uranus and Neptune move too slow.

Velocity	Average Velocity
It refers to the rate of change of position vector with respect to time.	It refers to the rate of change of displacement vector with respect to time
\(\overrightarrow { v } = \underset { \Delta t\rightarrow 0 }\lim { \frac { \Delta \overrightarrow { r } }{ \Delta t } } \)	\(\overrightarrow { v }_ {avg}=\frac { \Delta \overrightarrow { r } }{ \Delta t } \)