Prayas 2.0 Physics Quiz: Acceleration of a Particle with Time

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Questions and Answers

What is the incorrect graph representation of the same motion?

Graph C

Graph A

Graph B

Graph E (correct)

What is the distance traveled by a particle in time t, if its acceleration is increasing linearly with time t as bt, and it starts from the origin with an initial velocity v0?

v0t + bt^2/2 (correct)

v0t + bt/3

v0t + bt^2/3

v0t + bt/6

What is the distance covered by a ball thrown vertically upwards with speed u, during the last t seconds of its ascent?

ut - gt^2/2 (correct)

gt^2/2

(u + gt)t/2

What is the maximum velocity acquired by a car that accelerates from rest at a constant rate α for some time, and then decelerates at a constant rate β, and comes to rest in time t?

√(α^2 + β^2)t Signup and view all the answers

What is the resultant of two forces, each equal to F, acting as shown in Figure?

F Signup and view all the answers

What is the maximum height attained by a rocket, if its velocity variation with time is as shown in Figure?

55 km Signup and view all the answers

What is the reciprocal of the value of $2^3$?

1/12 Signup and view all the answers

What is the dimensional formula of heat energy?

MLT-1 Signup and view all the answers

What is the solution set of the inequality $2x^2 - 5|x| + 2 < 0$?

(-2, 2) Signup and view all the answers

If x, |x + 1|, |x - 1| are three terms of an arithmetic progression, then how many possible values of x are there?

2 Signup and view all the answers

What are the dimensions of the universal gravitational constant?

M-2 L2 T-2 Signup and view all the answers

What is the solution set of the inequalities |x - 1| ≤ 5 and |x| ≥ 2?

[-4, -2] ∪ [2, 6] Signup and view all the answers

What are the dimensions of v0 and a in the equation x = v0 (1 - e^(-at))?

M0 L T-1 and L T-2 Signup and view all the answers

What is the percentage error in the estimation of g, if the maximum percentage errors in the measurement of distance and time are e1 and e2 respectively?

e1 + 2e2 Signup and view all the answers

If (2x - 1) > 0, then what is the range of values for x?

x ∉ (0, 3/4) Signup and view all the answers

What is the maximum error in the estimation of kinetic energy, if the percentage errors in the measurement of mass and speed are 2% and 3% respectively?

11% Signup and view all the answers

What is the least positive integer that satisfies the inequality 2(x - 4) ≥ (x - 1)(x - 7)?

7 Signup and view all the answers

What is the physical quantity that is related to the pressure difference between the two ends of a tube of length l and radius r, through which turpentine oil is flowing?

Viscosity Signup and view all the answers

What is the volume occupied by one gram of a gas at STP if its vapour density is 11.2?

22.4 L Signup and view all the answers

If 50 atoms of carbon react with 200 molecules of oxygen, what is the correct statement?

O2 is the limiting reagent and 100 molecules of CO2 are formed Signup and view all the answers

A solution is prepared by adding 2g of substance A to 18g of water. What is the mass percent of the solute?

10% Signup and view all the answers

What is the number of moles of nitrogen atoms present in 112g of N2?

3.125 × 10^-2 Signup and view all the answers

What is the empirical formula of a hydrocarbon that contains 91.3% carbon by mass?

CH Signup and view all the answers

How many mL of 10 M HCl and 3 M HCl should be mixed to get 1 L of 6 M HCl solution?

479 mL and 521 mL Signup and view all the answers

What is the value of $2^2 \log_7 2 + \log_7 11$?

464 Signup and view all the answers

If $x^2 + 4y^2 + z^2 - 2xy - 2yz - zx = 0$, then what is the ratio of $x:y:z$?

1:2:1 Signup and view all the answers

If $\alpha$ is the smallest and $\beta$ is the largest integral solution of $x + 1 \leq x + 3x - 4(x + 5)$, then what is $\alpha + \beta$?

-1 Signup and view all the answers

What is the value of $49(1 - \log_7 2) + 5 - \log_5 4$?

2 Signup and view all the answers

What is the complete solution set of the inequality $3x^2 + 5x + 7 - 3x^2 + 5x + 2 > 1$?

(-a, -b] ∪ [-c, d) Signup and view all the answers

What is the value of $a + b + c + d$, where $3a = 4, 4b = 5, 5c = 6, 6d = 7, 7e = 8, 8f = 9$?

3 Signup and view all the answers

Study Notes

Motion

The acceleration of a particle is increasing linearly with time t as bt.
The particle starts from the origin with an initial velocity v0.
The distance traveled by the particle in time t will be:
- v0t + bt^2/2
- The distance traveled by a particle starting from rest and moving with an acceleration ms^-2, in the third second is 4m
If a ball is thrown vertically upwards with speed u, the distance covered during the last t seconds of its ascent is:
- ut - gt^2/2

Forces

Two forces, each equal to F, act in a particular direction.
Their resultant is:
- F
- √(F^2 + F^2) = √2F
A car accelerates from rest at a constant rate α for some time after which it decelerates at a constant rate β and comes to rest.
If the total time elapsed is t, then the maximum velocity acquired by the car will be:
- (αβt)/(α + β)

Graphs

The graph shows the variation of velocity of a rocket with time.
The maximum height attained by the rocket is:
- 1.1 km
- 5 km
- 55 km
- None of these

Algebra

The reciprocal of the value of 2^3 is:
- 3
- 4
- 5
- 6
The complete solution set of the inequation 2x^2 - 5|x| + 2 < 0, is:
- (-2, 2)
- [-2, -1] ∪ [1, 2]
- (-∞, -2] ∪ [2, ∞)
If x, |x + 1|, |x - 1| are three terms of an A.P., then the number of possible values of x is equal to:
- 0
- 1
- 2
- 3
Solution set of inequations |x - 1| ≤ 5, |x| ≥ 2 is:
- [-4, 6]
- (-∞, -2] ∪ [2, ∞)
- (-∞, -2] ∪ [2, 6]
- [4, 6]

Physics

Dimensional formula of heat energy is:
- ML^2T^-2
The dimensions of v0 and a are:
- M^0L^1T^-1 and T^-1
- M^0L^1T^0 and T^-1
- M^0L^1T^-1 and LT^-2
- M^0L^1T^-1 and T^1
If the maximum percentage errors in measurement of the distance and the time are e1 and e2 respectively, the percentage error in the estimation of g is:
- e1 + e2
- e1 - e2
- e1 + 2e2
- 2e1 - e2

Chemistry

The value of x in the formula (CO)x is:
- 1
- 2
- 3
- 4
To neutralize 20 mL of M/10 NaOH, the volume (in mL) of M/20 HCl needed is:
- 40
- 50
- 60
- 80
The molarity of 5.85 g of NaCl dissolved in H2O and solution made up to 500 mL is:
- 0.1 M
- 0.2 M
- 0.3 M
- 0.5 M

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Description

Practice your Physics skills with this multiple choice quiz, covering topics such as dimensional formulas, heat energy, and particle motion. Test your understanding of these fundamental concepts and get ready for your exams!

Prayas 2.0 2024 Physics Practice Test 01