NTA JEE Main 27th July 2022 Shift 1

A torque meter is calibrated to reference standards of mass, length and time each with $$5\%$$ accuracy. After calibration, the measured torque with this torque meter will have net accuracy of

A bullet is shot vertically downwards with an initial velocity of $$100 \text{ m s}^{-1}$$ from a certain height. Within $$10 \text{ s}$$, the bullet reaches the ground and instantaneously comes to rest due to the perfectly inelastic collision. The velocity-time curve for total time $$t = 20 \text{ s}$$ will be: (Take $$g = 10 \text{ m s}^{-2}$$)

A bag is gently dropped on a conveyor belt moving at a speed of $$2 \text{ m s}^{-1}$$. The coefficient of friction between the conveyor belt and bag is $$0.4$$. Initially, the bag slips on the belt before it stops due to friction. The distance travelled by the bag on the belt during slipping motion is: [Take $$g = 10 \text{ m s}^{-2}$$]

Sand is being dropped from a stationary dropper at a rate of $$0.5 \text{ kg s}^{-1}$$ on a conveyor belt moving with a velocity of $$5 \text{ m s}^{-1}$$. The power needed to keep belt moving with the same velocity will be

Two satellites $$A$$ and $$B$$ having masses in the ratio $$4:3$$ are revolving in circular orbits of radii $$3r$$ and $$4r$$ respectively around the earth. The ratio of total mechanical energy of $$A$$ to $$B$$ is

Two cylindrical vessels of equal cross-sectional area $$16 \text{ cm}^2$$ contain water upto heights $$100 \text{ cm}$$ and $$150 \text{ cm}$$ respectively. The vessels are interconnected so that the water levels in them become equal. The work done by the force of gravity during the process, is [Take density of water $$= 10^3 \text{ kg m}^{-3}$$ and $$g = 10 \text{ m s}^{-2}$$]

If $$K_1$$ and $$K_2$$ are the thermal conductivities, $$L_1$$ and $$L_2$$ are the lengths and $$A_1$$ and $$A_2$$ are the cross sectional areas of steel and copper rods respectively such that $$\dfrac{K_2}{K_1} = 9$$, $$\dfrac{A_1}{A_2} = 2$$, $$\dfrac{L_1}{L_2} = 2$$. Then, for the arrangement as shown in the figure, the value of temperature $$T$$ of the steel-copper junction in the steady state will be

Read the following statements:
A. When small temperature difference between a liquid and its surrounding is doubled the rate of loss of heat of the liquid becomes twice.
B. Two bodies P and Q having equal surface areas are maintained at temperature $$10°C$$ and $$20°C$$. The thermal radiation emitted in a given time by P and Q are in the ratio $$1:1.15$$.
C. A Carnot Engine working between $$100 \text{ K}$$ and $$400 \text{ K}$$ has an efficiency of $$75\%$$.
D. When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice.
Choose the correct answer from the options given below:

Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is $$1:4$$, then
A. The r.m.s. velocity of gas molecules in two vessels will be the same.
B. The ratio of pressure in these vessels will be $$1:4$$.
C. The ratio of pressure will be $$1:1$$.
D. The r.m.s. velocity of gas molecules in two vessels will be in the ratio of $$1:4$$.

Two identical positive charges $$Q$$ each are fixed at a distance of $$2a$$ apart from each other. Another point charge $$q_0$$ with mass $$m$$ is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge $$q_0$$ executes SHM. The time period of oscillation of charge $$q_0$$ will be