Choose a course and topic, attempt each question and open its complete worked solution when you are ready.
Which functional group occurs in butanone?
Butanone contains the internal carbonyl group \(\ce{>C=O}\), which defines a ketone.
Ketone - option (C).
What is an alloy?
An alloy is a homogeneous mixture of two or more metals, or of a metal with a non-metal, prepared to obtain useful properties. Brass is copper with zinc; steel is iron with carbon.
A homogeneous mixture of metals, or a metal and a non-metal.
Give the common name of \(\ce{CaOCl2}\).
The compound \(\ce{CaOCl2}\), commonly represented as calcium oxychloride, is known as bleaching powder.
Bleaching powder.
A \(1.00\,\mathrm{m}\) steel rod is clamped at its centre and vibrates longitudinally at its fundamental frequency 2.53 kHz. Find the sound speed in steel.
Principle. The clamp is a displacement node and the free ends are antinodes. Each half-rod is one quarter wavelength, so the full rod has L=λ/2.
Sound speed ≈ 5.06 × 10³ \(\mathrm{m\,s}\)⁻¹.
A pendulum of length l hangs in a car moving at speed v around a horizontal circle of radius R. Find the period of small radial oscillations.
Principle. In the car frame, the bob experiences gravity g downward and an outward pseudo-acceleration v²/R. The equilibrium string aligns with their vector resultant; small oscillations occur under its magnitude.
T = 2π√[l/√(g²+v⁴/R²)].
A \(30\,\mathrm{kg}\) child's temperature falls from 101°F to 98°F in 20 min solely because of extra sweat evaporation. Taking body specific heat as 1 cal g⁻¹ °C⁻¹ and Lv=580 cal g⁻¹, find the average extra evaporation rate.
Principle. Convert the Fahrenheit interval to Celsius, compute heat removed, then divide by latent heat and time.
Average extra evaporation ≈ \(4.31\,\mathrm{g}\) min⁻¹.
Three identical bearings are aligned on a frictionless table; one moving bearing strikes two touching stationary bearings head-on elastically. Select the physically possible final pattern.
Principle. Both momentum and kinetic energy constrain the result. For identical masses, transfer of speed V to the far bearing with the other two stopping satisfies both.
Judge three statements: (a) acceleration in any circular motion always points to the centre(b) instantaneous velocity is tangent to the path(c) average acceleration over a complete uniform circular revolution is zero.
Principle. Nonuniform circular motion can include tangential acceleration; velocity is the tangent derivative; average acceleration is delta-v over elapsed time.
From the sinusoidal position-time curve, give signs of position, velocity and acceleration at \(t=0.3\,\mathrm{s}\), \(1.2\,\mathrm{s}\) and \(-1.2\,\mathrm{s}\).
Principle. Velocity is the graph slope and simple harmonic acceleration has the opposite sign to displacement: a=-omega^2 x.
Explain why nearby scenery appears to sweep backward from a moving train while hills and celestial objects barely shift.
Principle. Apparent motion is governed by angular change at the eye, which for a small sideways displacement is inversely proportional to distance.