Physics
Question from maharashtra board physics book of 12th maharashtra board
- A solid sphere rolls without slipping on a horizontal surface. The fraction of its total kinetic energy that is rotational is Answer: B. 2/7 KE_rot=1/2·2/5 mR²ω²=1/5 mv² , KE_total=1/2mv²+1/5mv²=7/10mv² . Fraction =1/5/7/10=2/7 . 1
- A flywheel of moment of inertia 2 kg m2 is speeded up from 10 rad/s to 20 rad/s. The work done on it is Answer: D. 300 J W=Δ KE=1/2 I(ω₂²-ω₁²)=1/2(2)(400-100)=300 J. 1
- A curved road of radius 50 m is to be banked so that a car moving at 10 m/s needs no friction. The angle of banking is (g = 10 m/s2) Answer: C. tan⁻¹(0.2) tanθ=v²/rg=100/50×10=0.2 . 1
- A small stone tied to a string of length 0.9 m is whirled in a vertical circle. The minimum speed it must have at the lowest point to just complete the circle is (g = 10 m/s2) Answer: A. 6.7 m/s v_min=√(5gr)=√(5×10×0.9)=√(45)≈6.7 m/s. 1
- A circular coil of 100 turns and radius 10 cm carries a current of 5 A. The magnetic field at its centre is (\(\mu_0=4\pi\times10^{-7}\) T m/A) Answer: D. π×10⁻³ T B=μ₀NI/2R=frac4π×10⁻⁷×100×50.2=π×10⁻³ T. 1
- A proton and an α-particle having the same kinetic energy enter a uniform magnetic field perpendicular to it. The ratio of the radii of their circular paths \(r_p:r_\alpha\) is Answer: A. 1 : 1 r=√(2mK)/qB . For α: mass 4m , charge 2e gives √(8mK)/2eB=√(2mK)/eB , same as proton. 1
- A rectangular coil of 50 turns and area 0.02 m2 carries 2 A in a uniform field of 0.5 T. The torque on it when its plane is parallel to the field is Answer: B. 1 N m Plane parallel to field means the normal is perpendicular to B : τ=NIAB=50×2×0.02×0.5=1 N m. 1
- The magnetic susceptibility of a paramagnetic salt is \(\chi\) at 300 K. Its susceptibility at 200 K will be Answer: D. 1.5chi Curie's law: chi∝1/T⇒chi'=chi×300/200=1.5chi . 1
- A conducting rod of length 1 m moves at 5 m/s perpendicular to a uniform magnetic field of 0.4 T on frictionless rails connected through a 4 Ω resistor (other resistances negligible). The external force needed to keep it moving at constant speed is Answer: D. 0.2 N e=Blv=2 V, I=0.5 A, F=BIl=0.4×0.5×1=0.2 N. 1
- When the current in a coil falls uniformly from 2 A to zero in 0.05 s, an emf of 8 V is induced in it. The self-inductance of the coil is Answer: A. 0.2 H L=e/dI/dt=8/2/0.05=0.2 H. 1
- In a series LCR circuit, \(L=\frac{1}{\pi}\) H and \(C=\frac{1}{\pi}\) μF. The resonant frequency is Answer: A. 500 Hz f=1/2π√(LC)=frac12π·frac10⁻³π=500 Hz. 1
- In a series RL circuit, R = 30 Ω and \(X_L\) = 40 Ω. The power factor of the circuit is Answer: D. 0.6 Z=√(30²+40²)=50\ Ω , cosφ=R/Z=0.6 . 1
- Light of wavelength 310 nm falls on a metal of work function 2.5 eV. The stopping potential is (take \(hc=1240\) eV nm) Answer: C. 1.5 V E=1240/310=4 eV; eV₀=4-2.5=1.5 eV, so V₀=1.5 V. 1
- The de Broglie wavelength of an electron accelerated from rest through a potential difference of 100 V is about Answer: B. 1.227 Å λ=12.27/sqrt V Å =12.27/10=1.227 Å. 1
- The ratio of the wavelength of the first line of the Balmer series to that of the first line of the Lyman series in hydrogen is Answer: D. 27/5 frac1λ_B∝1/4-1/9=5/36 , frac1λ_L∝1-1/4=3/4 . λ_B/λ_L=3/4/5/36=27/5 . 1
- \({}^{238}_{92}\mathrm{U}\) decays to \({}^{206}_{82}\mathrm{Pb}\). The numbers of α and β− particles emitted are Answer: D. 8 α and 6 β α count =238-206/4=8 , lowering Z by 16 to 76. To reach 82, 6 β⁻ are needed. 1
- A 6 V Zener diode is used with a series resistance of 200 Ω across a 10 V supply. A load of 1 kΩ is connected across the Zener. The current through the Zener diode is Answer: C. 14 mA Series current =10-6/200=20 mA; load current =6/1000=6 mA; Zener current =14 mA. 1
- The excess pressure inside a soap bubble of radius 2 cm is (surface tension of soap solution = 0.03 N/m) Answer: C. 6 Pa A soap bubble has two surfaces: Δ P=4T/r=4×0.03/0.02=6 Pa. 1
- Eight identical rain drops, each falling with terminal velocity \(v\), coalesce to form a single drop. The terminal velocity of the big drop is Answer: A. 4v Volume conserved: R³=8r³⇒ R=2r . Since v_t∝ r² , new terminal velocity =4v . 1
- Water flows through a horizontal pipe whose cross-sectional area at a wide section is twice that at a narrow section. If the speed at the wide section is 2 m/s, the pressure difference between the wide and narrow sections is (density of water = 1000… Answer: C. 6000 Pa Continuity: v₂=2×2=4 m/s. Bernoulli: Δ P=1/2ρ(v₂²-v₁²)=500(16-4)=6000 Pa. 1
- The r.m.s. speed of the molecules of a gas at 27 °C is \(v\). The temperature at which the r.m.s. speed becomes \(2v\) is Answer: D. 927 °C v_rms∝√(T) : T₂=4×300=1200 K =927 °C. 1
- If the absolute temperature of a perfect black body is doubled, the energy radiated by it per second becomes Answer: B. 16 times Stefan's law: E∝ T⁴ , so 2⁴=16 times. 1
- The wavelength of maximum emission from the sun is 480 nm. Taking Wien's constant \(b=2.88\times10^{-3}\) m K, the surface temperature of the sun is Answer: C. 6000 K T=fracbλ_max=frac2.88×10⁻³480×10⁻⁹=6000 K. 1
- An ideal gas has density 1.2 kg/m3 at a pressure of \(1\times10^5\) Pa. The r.m.s. speed of its molecules is Answer: B. 500 m/s P=1/3ρ v_rms²⇒ v_rms=√(3P/ρ)=√(3×10⁵/1.2)=500 m/s. 1