Physics
Question from maharashtra board physics book of 12th maharashtra board
- One mole of an ideal gas expands isothermally at 300 K to twice its initial volume. The work done by the gas is approximately (R = 8.314 J mol-1 K-1, ln 2 = 0.693) Answer: B. 1729 J W=nRTlnV₂/V₁=8.314×300×0.693≈1729 J. 1
- A Carnot engine has efficiency 40% with its sink at 300 K. Keeping the sink temperature constant, by how much should the source temperature be increased to raise the efficiency to 50%? Answer: C. 100 K 0.4=1-300/T₁⇒ T₁=500 K. For 50%: T₁'=600 K. Increase =100 K. 1
- The displacement of a particle in SHM is \(x=5\sin\left(\pi t+\frac{\pi}{3}\right)\) cm. Its maximum speed is Answer: B. 5π cm/s v_max=Aω=5×π=5π cm/s. 1
- A mass attached to a spring oscillates with period \(T\). The spring is cut into two equal halves and the same mass is attached to one half. The new period is Answer: D. T/sqrt2 Half spring has k'=2k . T∝1/sqrt k⇒ T'=T/sqrt2 . 1
- The fundamental frequency of a pipe closed at one end is 250 Hz. The frequency of its first overtone is Answer: D. 750 Hz A closed pipe has only odd harmonics; first overtone =3n=750 Hz. 1
- A tuning fork of frequency 256 Hz produces 4 beats/s with an unknown fork. When the unknown fork is loaded with a little wax (which lowers its frequency), the number of beats becomes 6 per second. The original frequency of the unknown fork is Answer: A. 252 Hz Unknown is 252 or 260 Hz. Loading lowers frequency; beats increase only if it was already below 256, so it is 252 Hz. 1
- A string 1 m long, fixed at both ends, carries transverse waves with speed 200 m/s. The frequency of its second overtone is Answer: A. 300 Hz Fundamental =v/2L=100 Hz; second overtone = third harmonic =300 Hz. 1
- In Young's double slit experiment, slit separation is 0.5 mm, the screen is 1 m away and \(\lambda=600\) nm. The fringe width is Answer: A. 1.2 mm β=λ D/d=frac600×10⁻⁹×10.5×10⁻³=1.2×10⁻³ m. 1
- The polarising (Brewster) angle for a glass of refractive index \(\sqrt3\) is Answer: D. 60° tanθ_p=μ=sqrt3⇒θ_p=60^° . 1
- Light of wavelength 500 nm falls normally on a single slit of width 0.2 mm. The width of the central maximum on a screen 2 m away is Answer: D. 10 mm W=2λ D/a=frac2×5×10⁻⁷×22×10⁻⁴=10⁻² m =10 mm. 1
- In a metre bridge, a 2 Ω resistance is in the left gap and an unknown resistance \(X\) in the right gap. The null point is at 40 cm from the left end. Then \(X\) is Answer: D. 3 Ω 2/X=40/60⇒ X=3\ Ω . 1
- A potentiometer wire 4 m long of resistance 8 Ω is connected in series with a 12 Ω resistor and a 2 V cell of negligible internal resistance. The balancing length for a cell of emf 0.5 V is Answer: C. 2.5 m I=2/20=0.1 A; potential gradient =0.1×8/4=0.2 V/m; l=0.5/0.2=2.5 m. 1
- A galvanometer of resistance 50 Ω gives full-scale deflection for 5 mA. The shunt needed to convert it into an ammeter of range 0–5 A is approximately Answer: D. 0.05 Ω S=I_gG/I-I_g=0.005×50/4.995≈0.05\ Ω . 1
- A 100 µF capacitor is charged with a 50 V source supply. Then source supply is removed and the capacitor Data: C = 100 µF = 100 × 10⁻⁶ F = 10⁻⁴ F, V = 50V, i = 5A The energy stored in the electric field in the capacitor = 1/2 CV² The energy stor... 1
- Compare resistance and reactance. Resistance Reactance It is a property of a material or component that opposes the flow of current through it. It is a property of a material... 1
- What is the natural frequency of L C circuit ? What is the reactance of this circuit at this frequency The natural frequency of LC circuit is 1/2 π √(L C) , where L is the inductance and C is the capacitance. The reactance of this circuit at t... 2
- What is wattless current ? The current that does not lead to energy consumption, hence zero power consumption, is called wattless current. In the case of a purely indu... 1
- For very high frequency AC supply, a capacitor behaves like a pure conductor. Why ? The reactance of a capacitor is XC = 1/2 π f C , where f is the frequency of the AC supply and C is the capacitance of the capacitor. For ve... 1
- The total impedance of a circuit decreases when a capacitor is added in series with L and R. Explain why ? For an LR circuit, the impedance, Z_LR = sqrtR²+X_L² , where X_L is the reactance of the inductor. When a capacitor of capacitance C is adde... 1
- An electric lamp is connected in series with a capacitor and an AC source is glowing with a certain brightness. Answer: The lamp glows more brightly when the capacitance is increased. For the lamp (resistance R) in series with a capacitor C on an AC su... 1
- A toroidal ring, having 100 turns per cm of a thin wire is wound on a nonmagnetic metal rod of length 1 m and diameter Data : l = 1 m, d = 1 cm, n = 100 cm⁻¹ = 10⁴ m⁻¹, I = 100 A, µ₀ = 4π × 10⁻⁷ H/m The radius of cross section, r = d/2 = 0.5 cm = 5 × 10⁻³ m (... 2
- The primary and secondary coil of a transformer each have an inductance of 200 × 10-6H. Data: L_P = L_S = 2 × 10⁻⁴ H, M = 4 × 10⁻⁶ H M = K sqrtL_P L_S The coupling coefficient is K = fracMsqrtL_P L_S=frac4 × 10⁻⁶sqrt(2 × 10⁻⁴)²=... 1
- A long solenoid of length l, cross-sectional area A and having N1 turns (primary coil) has a small coil of N2 We assume the solenoid to be ideal and that all the flux from the solenoid passes through the outer coil C. For a steady current Is through... 1
- An emf of 96.0 mV is induced in the windings of a coil when the current in a nearby coil is increasing Data: |e₂| = 9.6 × 10⁻² V, dI₁/dt = 1.2 A/s |e₂| = M fracd I₁d t Mutual inductance, M = frac|e₂|d I₁ / d t=frac9.6 × 10⁻²1.2 = 8 × 10⁻² H =... 1