In the equation y = y0 + vt + 1/2at^2 y and y0 are distances, v is a velocity, a is an acceleration, and t is time. Is the equation dimensionally homogeneous?

Q: Check which equations are dimensionally correct or incorrect: v is velocity, m is mass, g is…

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Q: Consider the physical quantities s, v, a, and t with dimensions [s] = L, [v] = LT−1, [a] = LT−2, and…

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Q: The period of a pendulum is the time it takes the pendulum to swing back and forth once. If the only…

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Q: The quantity with the same units as force times time, Ft, with dimensions MLT -1 is A mv B my 2r C)…

A: Given data The dimensions of the force times time is MLT-1. Checking the dimensions of formulae’s…

Q: Show that v² = v} +2ax is dimensionally consistent. Here v is velocity, x is distance and a is…

A: Considering the LHS of the equation, v2=LT-12=L2T-2

Q: 4. Fill the Table 2 with the equivalent quantity by conversion the following physical quantities…

A: Given, 1 lbf=4.45 N, 1 ft=0.3048 m, 1 hr=3600 s, 1 psi=6894.76 Pa, 1 mi=1.69 km, and 1 in=2.45 cm.

Q: Consider the equation s = s0 + v0t + a0t2/2 + j0t3/6 + S0t4/24 + c0t5/120 , where s is length, and t…

A: As S is length So dimension of S is [L] so dimension of right side terms must be [L].

Q: A cylinder of mass (m) and a diameter of (2a) with height (10 cm), The height for other cylinder…

A: Since the cylinders are made of the same material, the density of the material must be constant. The…

Q: A rather ordinary middle-aged man is in the hospital for a routine check-up. The nurse writes the…

A: Dear student For a middle aged man, the mass could be around 70kg, and age would be around 45 years.

Q: What is the value of Xc (in centimeters) if R is 15cm?

A: Given,Radius of the quater plate, R = 15 cm

Q: How many significant figures does  1.362+25.2 have ? (a) 2.             (b) 3.              (c) 4.…

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Q: In the equation below, which (if any) of the terms are not dimensionally consistent with the others?…

A: The dimension of mass m is [m]=M. The dimension of gravitational constant g is [g]=LT-2. The…

Q: Show that x = x0 + v0t + 12 at2 is dimensionally consistent. The quantities x and x0 aredistances,…

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Q: If a is acceleration, v is velocity, x is position, and t is time, then which equation is not…

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Q: If a is acceleration, v is velocity, x is position, and t is time, then which equation is not…

A: Answer From first option the dimension of time is given by t = T From second option a = v2/x  The…

Q: Why is it km and not meters, if c = 3x10^8 m and G has meter in the constant

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Q: If equation F = m.g + A.m is assumed to be dimensionally correct, then dimension of quantity A will…

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Q: What are the units (in the SI system) of a physical quantity whose dimensions are L²M'T-3? kg/s³ |…

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Q: Consider the physical quantities m, s, v, a, and t with dimensions [m] = M, [s] = L, [v] = LT–1, [a]…

A: Using dimension analysis,   Dimension of L.H.S = Dimension of R.H.S

Q: 1). Density describes a. mass per unit volume. b. length per unit time. C. volume per liter. d.…

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Q: Calculate the probable error in the volume of the container, in m3

A: Volume of rectangular prism = L W H

Q: Assume: r, x, x0 have units of m. v, vO have units of m/s. a has units of m/s/s. m, m1, m2 have…

A: Dimensions are defined as the minimum number of coordinates required to specify the magnitude of any…

Q: QUESTION 2 Match units with physical quantities. m = meter kg = kilo gram s= second Mass (M) v…

A: We know, S.I. unit of mass (M) is kilogram (kg) S.I. unit of length (or distance, L) is meter (m)…

Q: A block of iron has dimensions 2 mx 0.5 m × 0.25 m. The density of iron is 7.8 g cm-³. Find the mass…

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Q: The position of a moving particle in vortex is expressed as, x(t) = x0 sin(at3 + bt3/2) where x0is…

A: x(t)=x0Sin(at3+bt3/2)Sin is a transcendental function. Its argument has to be dimensionless.Since…

Q: Calculate to the correct number of significant figures: 2.346 + 24.128 = 38.4 x 128.45 = Verify if…

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Q: P V =

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Q: Each of the following equations was given by a studentduring an examination: (a) 1/2 mv2= 1/2 mvo2 +…

A: Given:(a) 1/2 mv2= 1/2 mvo2 + √mgh(b) v= v0 +at2(c) ma =v2

Q: The average cost per unit P(x) in pesos, в 0.67 to produce x units of cellphone is 300 given by P(x)…

A: NOTE : As per bartleby guidelines, we can answer only first question. For remaining questions please…

Q: A can of tomatoes has a radius of 6 cm and a height of 10 cm. What is the approximate volume of the…

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Q: In meters, what is the displacement traveled fromt = 10 sec to t = 25 sec? To correctly calculate…

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Q: Which of the following equations are dimensionally (units) consistent? 1. v = 1/2at2 2. t = v/a…

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Q: Somewhere, time is measured in cronosees (c) and distance is measured in tsols (t). The conversion…

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Q: The period of a simple pendulum, defined as the time necessary for one complete oscillation, is…

A: The expression for the time period is,

Q: What is the smallest quantity that can be weighed on a scale that has a sensitivity requirement of 5…

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Q: In the equation F= xt' +yt?. F = Force and t = time. The dimensions of x and y respectively are Oa…

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Q: In one of the labs, a student found the length and width of a rectangular wooden board. The recorded…

A: As per Bartleby guidelines I have solved first question out of multiple questions and if you want…

Q: Use the dimensional analysis to show if the following equations below are dimensionally consistent:…

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Q: If the distance dd (in meters) traveled by an object in time tt (in seconds) is given by the formula…

A: Given data:  Distance d in meters d = A + Bt2  Time (t) in seconds  Required: The SI units of A and…

Q: Using dimensional analysis, check which of the following equations is or are correct. 1. a=v/t 2.…

A: Given  1. a=v/t 2. density = mass/volume 3. speed = d/t^2  4. a=∆v/∆t

Q: Which of the following equations are dimensionally consistent? (a) v = at, (b) v = 12at2, (c) t =…

A: a V=at     For dimensional stability , both side should have same dimensions .   LT-1=LT-2T…

Q: In the expression T= 2x. m has dimensions of mass and k has dimensions of mass divided by time…

A: Here, we calculate the given as follow;

Q: If you tried to smuggle gold bricks by filling your backpack, whose dimensions are 63 cm x 25 cm x…

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Q: The SI base units have the dimensions of: O mass, length, speed O weight, length, time O length,…

A: Let's check each option one by one 1. Mass , length , speed Not correct  Since speed is a derived…

Q: In the equation, C, = pgy+0.5pC,), if y is distance, g is gravitational acceleration, p density and…

A: For the equation C1=ρgy+0.5ρC22 to be dimensionally correct, each term in the equation must have the…

Q: A student measures the thickness of a textbook with a meter stick and obtains a value of 3.8 cm ±0.1…

A: Option (b) agree with the value of the first student. i e  3.81 cm ±0.01 cm

Q: Which of the following relationships is dimensionally consistent with an expression yielding a value…

A: Given data:  Acceleration = distance /(Time)2 x is distance t is time V is velocity

Q: Consider the physical quantities s, a, and t with dimensions [s] = L, [v] = LT-!, [a] = LT -2, v,…

A: Dear student According to dimensional analysis, only the quantities which have same dimensions can…

Q: The volume of the rectangular block in the figure is calculated from the following measurements of…

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Q: Each of the following equations was given by a student during an examination. Do a dimensional…

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Units and Dimensions

These are generally defined as the terms which precede or describes the dimensions further. These are also further divided into two parts namely fundamental units and the derived units.