Easy & Concise NCERT Physics Ch-1,2,3 : All Exercises Solved

Convert meters to light years using the unitary method and the speed of light, showing one meter equals 1.0569e-16 light years based on 31,536,000 seconds per year.

Compute area on slide and area on screen, derive area magnification from their ratio, and obtain linear magnification as the square root in q1.9.

Assess the number of significant figures in six items, and apply rules: ignore leading zeros, count trailing zeros in decimals, and count coefficient digits in scientific notation.

Derive the relativistic mass formula m = m0 / sqrt(1 - v^2/c^2) by dimensional analysis, confirming kilogram units and the dimensionless v^2/c^2.

Explain why nearby objects move opposite to a fast train while distant objects seem stationary due to parallax, and show the Sun's density is close to that of liquids.

Use time equals distance over speed on the xt graph to model a 2.5 km office trip at 5 km/h, with return at 25 km/h.

Trace the x-t graph to follow alternating forward and backward steps in 8-second intervals, revealing the pitfall region and ending with a fall into the pit at 37 seconds.

Examine a ball dropped from 90 meters, losing 10% speed at each floor collision, and plot speed-time graph showing 42 m/s at the first impact and 37.8 m/s after bounce.

Explain a one-dimensional xd plot where the particle rests for t<0 and accelerates after t=0, like a ball falling under gravity, and state the bullet’s impact speed as 105 m/s.

Analyze signs of position, velocity, and acceleration in one-dimensional simple harmonic motion using an x-t plot, noting negative x yields negative velocity and positive acceleration.

The XT plot shows average speed is greatest in interval 3 and least in interval 2; the slope is negative for interval 3 and positive for interval 2.

Analyze the speed-time graph to identify interval 2 as the greatest average acceleration and interval D as the greatest average speed. Confirm that the velocity remains positive in all intervals.

Identify the two scalar quantities in the list, noting scalars have only magnitude. Work and current are scalars, while the others are vectors.

Identify which scalar and vector operations are meaningful: scalar addition, scalar–vector incompatibility, vector scaling, scalar–scalar multiplication, adding two vectors, and adding a vector component to the same vector.

Evaluate true or false statements about vectors, including magnitude as a scalar, vector components, displacement versus total path length, average speed versus average velocity, and coplanar vectors.

Demonstrate |a+b| ≤ |a|+|b| and |a+b| ≥ ||a|-|b|| for vectors a and b; equality occurs when the vectors align or oppose.

Show that |a−b|^2 = |a|^2 + |b|^2 − 2|a||b|, revealing that |a−b| ≥ ||a| − |b|| with equality when a and b point in the same direction.

Relate A+B+C+D=0 to A,B,C,D being vectors or quadrilateral sides; |A+C|=|B+D|, |A|≤|B|+|C|+|D|, and B+C lies in the plane of A and D.

Analyze net displacement, average velocity, and average speed for a cyclist who travels from the circle center to the edge, along a quadrant, and back in 10 minutes.

Analyze vertical motion under gravity: determine downward acceleration during upward motion, zero velocity at the peak, and acceleration at the highest point; apply sign conventions for position, velocity, and acceleration.

Compare average speed and average velocity for a 23 km route traveled in 28 minutes. Apply projectile motion formulas to determine height and range for a 40 m/s throw.

Explore statements about circular motion: net acceleration is not always toward the center due to tangential components; velocity is tangent, and average acceleration in uniform circular motion is zero.

From r = 3T i − 2T^2 j + 4k, obtain v = 3 − 4T and a = −4; at T = 2 s, v = −5 m/s.

Particle starts at origin with velocity 10 j and acceleration 8 i + 2 j in xy plane; at t=2 s, x=16m, y=24m, speed 21.4m/s.

Compute magnitudes and components of A=2i+3j along i+j and i−j using dot product; |i+j|=|i−j|=√2 and |A|=√13, giving components 5/√2 and −1/√2 along those directions.