BITSAT Practice Test - 1 - JEE MCQ

To find the power delivered by the motor, we can use the formula:

Power = Torque × Angular speed

First, we need to convert the rotational speed from r.p.s (revolutions per second) to radians per second. There are 2π radians in one revolution, so:

Angular speed = 20 r.p.s × 2π radians/revolution = 40π radians/second

Now, we can plug the values into the formula:

Power = 75 N-m × 40π radians/second = 3000π Watts

Approximating π as 3.14, we get:

Power ≈ 3000 × 3.14 Watts ≈ 9420 Watts

So, the approximate power delivered by the motor is 9420 Watts.

Main Source of Solar Energy: Fusion Reactions

Solar energy, which is harnessed from the sun, primarily comes from fusion reactions that occur in the sun's core. Fusion reactions involve the combining of two light atomic nuclei to form a heavier nucleus, releasing a large amount of energy in the process. This is the process that powers the sun and provides the Earth with the energy we receive in the form of sunlight.

Key Points:

- Fusion reactions in the sun's core involve the fusion of hydrogen atoms to form helium.
- These reactions release a tremendous amount of energy in the form of heat and light.
- The energy produced in the sun's core is radiated outwards in the form of sunlight.
- Solar panels on Earth capture this sunlight and convert it into usable electricity for various applications.

Overall, fusion reactions in the sun are the main source of solar energy that we harness and utilize for various purposes on Earth.

Explanation:

Thermal Coefficient of Resistance:
- The resistance of a material changes with temperature due to the temperature coefficient of resistance.
- For most metals like Aluminum, the resistance decreases as temperature increases.
- For semiconductors like Germanium, the resistance increases as temperature increases.

Cooling from T1 to T2:
- When both Aluminum and Germanium are cooled from T1 to T2, their resistances will change according to their respective temperature coefficients.
- Aluminum's resistance will decrease as it is a metal, and its resistance decreases with decreasing temperature.
- Germanium's resistance will increase as it is a semiconductor, and its resistance increases with decreasing temperature.

Conclusion:
- Therefore, the correct option is C: Aluminum decreases and that of Germanium increases.

We know that capacitance, c = Kε₀A / d
Thus we get when K = 1 and d = 0.4 we get c = 2F
Thus let the value of c when K = 2.8 and d = 0.2 be z
Thus we get z/2 = (1 / 0.4) / (2.8 / 0.2) 
Thus we get z = 2 x 5.6 F
= 11.2 F

Force of static friction f = μR
or f = mg sin θ, on point of sliding down of body.
∴ f = 10 x g x sin 30^o
= 5(g) N = 5 kg wt.

Explanation:

- When the current in a moving coil galvanometer is increased by 1%, the magnetic field strength created by the current also increases by 1%.
- The deflection of a moving coil galvanometer is directly proportional to the magnetic field strength.
- Therefore, an increase of 1% in current will result in a 1% increase in the deflection of the galvanometer.

Therefore, the percentage increase in deflection will be 1%. Hence, option A is correct.

Explanation:

• For a particle in a uniformly accelerated circular motion, the velocity is transverse to the radius of the circle. This means that the velocity is perpendicular to the radius of the circle at any point in time.


• The acceleration of the particle in this motion has both radial and transverse components. The radial component of acceleration is directed towards the center of the circle, while the transverse component is perpendicular to the velocity and directed tangentially to the circle.


• Therefore, in a uniformly accelerated circular motion, the velocity is transverse and the acceleration has both radial and transverse components.


 

If the beam is horizontal, the apparent weight 

Solution:

- Given that potential energy is one-fourth of total energy when displacement from the mean position is x.
- Total energy in S.H.M is the sum of kinetic energy and potential energy.
- At any point in S.H.M, total energy E = K.E + P.E = 1/2 kx² + 1/2 kA₀²
- Given that at the point where potential energy is one-fourth of total energy, P.E = 1/4 E
- Therefore, 1/2 kx² = 1/4 (1/2 kx² + 1/2 kA₀²)
- Simplifying the equation, we get 2x² = x² + A₀²
- Therefore, x² = A₀²
- Taking square root on both sides, x = A₀
- Hence, the displacement from the mean position where potential energy is one-fourth of its total energy is A₀.

Therefore, the correct answer is B: A₀/2.

Correct Answer : d

Explanation :  Generator of axis of a cylinder is a line lying on its surface and parallel to axis of cylinder

By parallel axis theorem

I = (MR² ) /2 + MR²

= 3/2MR²

Explanation:

• When the gymnast lowers his hands while sitting on a rotating stool, the moment of inertia decreases. This is because the distribution of mass is closer to the axis of rotation, leading to a decrease in moment of inertia.


• As the moment of inertia decreases, according to the conservation of angular momentum, the angular velocity of the gymnast increases. This is because angular momentum is conserved and is the product of moment of inertia and angular velocity.


 

Therefore, the correct statements are:
2. The angular velocity increases.
3. The moment of inertia decreases.