ABHYAS · CLASS 9 STUDENTS (CBSE AND STATE BOARDS) PRACTISING SCIENCE NUMERICALS
Class 9 Science कक्षा 9 विज्ञान
Unlimited Class 9 science numericals with hints and worked steps: motion and equations of motion, velocity–time graphs, force and momentum, gravitation and free fall, work, energy and power, sound and echoes, atoms and molecules (molecular mass and the mole concept), density and pressure.
Motion
- Speed, distance and timeAverage speed = total distance ÷ total time. To change km/h to m/s multiply by 5/18; m/s to km/h multiply by 18/5.
- Acceleration and retardationAcceleration a = (v − u) ÷ t, in m/s². A negative value means the body is slowing down (retardation).
- Equations of motionFor uniform acceleration: v = u + at, s = ut + ½at², v² = u² + 2as. List u, v, a, t, s and pick the equation with one unknown.
- Distance from a velocity–time graphThe area under a velocity–time graph equals the distance travelled (for motion in one direction). Split it into rectangles and triangles.
Force and laws of motion
- Newton's second law (F = ma)Net force = mass × acceleration. 1 N is the force that gives a 1 kg mass an acceleration of 1 m/s².
- Momentum and its conservationMomentum p = mv (kg m/s). In a collision or explosion with no external force, total momentum before = total momentum after.
- Force from change in momentumForce = change in momentum ÷ time (F = m(v − u)/t). Increasing the time of impact reduces the force — that is why fielders pull their hands back.
Gravitation
- Mass and weight (Earth, Moon, planets)Weight W = mg. Mass stays the same everywhere; weight changes with g. On the Moon g is about 1/6 of g on Earth.
- Free fall under gravityA freely falling body has acceleration g (take 10 m/s² unless told otherwise). Use v = gt, h = ½gt², v² = 2gh for a body dropped from rest.
- Universal law of gravitation (scaling)F = G m₁m₂ / r². Force is proportional to each mass and inversely proportional to the square of the distance.
Work and energy
- Work done by a forceWork = force × displacement in the direction of the force (W = Fs), in joules. Lifting a load: W = mgh.
- Kinetic and potential energyKE = ½mv², PE = mgh. For a falling body (no air resistance) PE lost = KE gained, so v = √(2gh).
- Power and the kilowatt hourPower = work ÷ time (watts). 1 kWh = energy used by a 1000 W appliance in 1 hour = 3.6 × 10⁶ J; this is the "unit" on electricity bills.
Sound
Atoms and molecules
- Molecular mass and formula unit massAdd the atomic masses of all atoms in the formula (count subscripts carefully). For ionic compounds this sum is called the formula unit mass.
- Mole concept: mass, moles and particlesmoles = mass ÷ molar mass; number of particles = moles × 6.022 × 10²³ (Avogadro constant).