A rectangular block of dimensions 10 cm × 20 cm × 30 cm is floating in water. Which orientation is most stable?
Answer: C
Stability increases with larger base area and lower center of gravity. The 20×30 cm face down provides the largest base area, ensuring maximum stability.
Q.42Medium
A 4 kg block on a rough horizontal surface experiences friction force f = 12 N when moving. If pushed with force 20 N, what is the kinetic energy after traveling 5 m from rest?
Answer: B
Net force = 20 - 12 = 8 N. Work done by net force = 8 × 5 = 40 J. This equals KE gained = 40 J
Q.43Medium
A 6 kg object is subject to two perpendicular forces: F₁ = 8 N and F₂ = 6 N. What is the magnitude of acceleration?
A ball is thrown vertically upward with velocity 30 m/s. At what time does it return to the ground level? (g = 10 m/s²)
Answer: B
Using s = ut + ½gt² for complete journey (s=0): 0 = 30t - 5t². Solving: t(30 - 5t) = 0, giving t = 6 s (non-zero solution)
Q.45Medium
Two blocks A (mass 3 kg) and B (mass 2 kg) are connected by a light string over a frictionless pulley. Block A is on a smooth horizontal surface and B hangs vertically. What is the acceleration of the system? (g = 10 m/s²)
Answer: A
For Atwood-like system with one block horizontal: a = (m_B × g)/(m_A + m_B) = (2 × 10)/(3 + 2) = 520 = 4 m/s²
Advertisement
Q.46Medium
A particle of mass m undergoes motion with velocity v(t) = 3t² + 2t (in m/s). What is the net force on the particle when t = 2 s, if m = 2 kg?
Answer: A
Acceleration a = dv/dt = 6t + 2. At t=2s: a = 6(2) + 2 = 14 m/s². Force F = ma = 2 × 14 = 28 N
Q.47Medium
A gas undergoes an isothermal process at 300 K. If the initial volume is 2 L and final volume is 5 L, what is the work done by the gas? (Take R = 8.314 J/(mol·K), n = 1 mol)
In an adiabatic process with a diatomic ideal gas (γ = 1.4), if the initial temperature is 300 K and volume increases by factor of 2, what is the final temperature?
A cyclic process consists of two isothermal and two adiabatic processes (Carnot cycle). What is true about the heat exchanges?
Answer: A
In Carnot cycle, isothermal processes involve heat exchange with reservoirs (Q₁ at hot reservoir, Q₂ at cold reservoir), while adiabatic processes have no heat exchange (Q=0)
Q.50Medium
In an isobaric process, 5 moles of a monoatomic ideal gas are heated from 300 K to 400 K. What is the heat supplied? (R = 8.314 J/(mol·K))
For a van der Waals gas, which statement is correct?
Answer: A
Van der Waals equation (P + a/V²)(V - b) = RT accounts for molecular volume (b term) and intermolecular attractive forces (a term)
Q.55Medium
In an expansion process, a gas does 500 J of work and absorbs 300 J of heat. What is the change in internal energy?
Answer: A
Using first law: ΔU = Q - W = 300 - 500 = -200 J (internal energy decreases)
Q.56Medium
During an isobaric expansion of an ideal gas, the work done by the gas is 400 J. If pressure is constant at 2 atm, what is the change in volume? (1 atm = 101325 Pa)
Answer: B
W = PΔV. Here W = 400 J, P = 2 × 101325 = 202650 Pa. So ΔV = W/P = 202650400 ≈ 0.00197 m³
Q.57Medium
For a diatomic ideal gas undergoing an isothermal process, which quantity remains constant?
Answer: C
In an isothermal process, temperature is constant. For an ideal gas, internal energy depends only on temperature, so ΔU = 0. Pressure and volume change according to PV = constant.
Q.58Medium
Two samples of the same ideal gas at the same temperature have volumes V and 2V respectively. The ratio of their internal energies is:
Answer: D
Internal energy U = nCvT. Without knowing the number of moles in each sample, the ratio cannot be determined. Same temperature doesn't mean same internal energy.
Q.59Medium
A heat engine absorbs 1000 J of heat and rejects 600 J to the cold reservoir in one cycle. What is its efficiency?
