Problem 12: In this problem, the symbols M, L, and T represent the dimensions mass, length, and time, respectively. Consider the physical quantities V, ρ, and t with dimensions [V] = L3, [ρ] = ML-3, and [t] = T. (Here, the square bracket means “the dimensions of” so, for example, [V] represents the dimensions of the quantity V.) Part (a) What are the dimensions of ∫ρdV? dimensions = ______ Part (b) What are the dimensions of dV/dt? dimensions = ______ Part (c) What are the dimensions of ρ(dV/dt)? dimensions = ______

Q: A potato of mass m = 0.26 kg hangs motionless, suspended by two strings as in the figure. Find the…

A: The mass of the potato:

Q: A pulley, which can be modelled as a solid cylinder, has a total mass of 14 kg and a radius of 20…

A:

Q: A sphere of radius r has surface area A = 4πr2 and volumeV = (4/3)πr3. If the radius of sphere 2 is…

A: a)The ratio of the areas, A2/A1

Q: Consider the physical quantities s, t, u, v and w. We would like to work with these quantities using…

A: Here we have to make a formulation of the given quantities in the mathematical model. So, we…

Q: Calculate the value of the error with one decimal place for the multiplication of x and y: z=xxy…

A:

Q: acceleration due

A: We say formulas used in physics are consistent with SI unit. The quantities that are independent of…

Q: Newton’s second law states that the acceleration of an object is proportional to the force F acting…

A: The dimensions of force can be derived from Newton's second law. The equation is, a = F/m, where a…

Q: Problem 3: A truck with 0.420 m radius tires travels at 42 m/s. Randomized Variables v = 42 m/s

A: Velocity, V=42m/s radius, r=0.420m from the relation V=Wr, where W =angular velocity  so W=V/r…

Q: undergo many adventures as they travel the Earth's oceans. (a) If 1.00 league equals 3.500 km, find…

A:

Q: Perform the following unit conversions: a) 65 miles per hour to meters per second (hint: 1 mile =…

A:

Q: The measurement error is defined as AX=X-Xo where Xo is the true value of a physical quantity. X is…

A: The true value of the physical quantity is X0 and the measured value of physical quantity is X.…

Q: For about 10 years after the French Revolution, the French government attempted to base measures of…

A:

Q: An object with a mass of 61.0 g displaces 785.0 ml of water when it is completely immersed. What is…

A: Mass = 61  Volume = 785 mL Fbuoyant = Fb = rho*V*g = 10^-3*785*9.8 = 7.693 N

Q: fine grains of beach sand are assumed to be spheres of radius a. 45.7 μm. These grains are made of…

A: Given data: The diameter of each grain is, The density of the silicon dioxide grain is, Formula…

Q: I'm not understanfing part b of this homework problem.

A: (a)Standard week consists,

Q: (a) What is the area and uncertainty in area of one side of a rectangular wooden board that has a…

A:

Q: Carry out the following arithmetic operations. (Enter your answers to the correct number of…

A: In the measured value of the physical quantity the number of digits about the correctness of which…

Q: Problem 2: A rectangular box is h= 14 inches in height, w = 26.5 cm wide, and L = 1.9 yards long.…

A:

Q: Q6: Suppose your hair grows at the rate 1/32 in per day. What is the rate at which it grows in…

A: Given Hair grows at a rate r=132 in/day   We have to convert the rate in nm/s1 d=86400 s

Q: Working the answers from the previous question, what would be the relative uncertainty of the area?…

A: Given: Length of the wooden board L=35.7 cm Width of the wooden board W=28.6 cm Uncertainty in…

Q: An expression for buoyant force is FB = ρgV, where FB has dimensions [MLT−2], ρ (density) has…

A: Buoyant Force is given by FB = ρgV FB is Buoyant Force which has dimensions [MLT−2] where ρ is…

Q: On planet Z, the standard unit of length is the foose. Ann the Astronaut is 5.2 feet tall on Earth.…

A: Given Height of Ann on Earth is HAnn, earth=5.2 ft Height of Ann on planet Z is HAnn, Z=88 foosi…

Q: We would like to find a relationship between the physical quantities s, t, u and v using theorem.…

A: Given Data: The given equation is  satbucvd i.e.  MLT2aT/LbM2T2cL2d   and  2a+?b+2c = 0

Q: Problem 2. Kinetic energy K has dimensions kg m²/s². It can be written in terms of the momen- um p…

A:

Q: ds and a = dt dv Suppose quantity s is a length and quantity t is a time. Suppose the quantities v…

A:

Q: The relationship between three quantities x, y, and z is given by x = y² /z. If the dimension of y…

A: Given: The relationsp between quanittity is. x=y2z The dimension of the y is LT. The dimension of…

Q: For about 10 years after the French Revolution, the French government attempted to base measures of…

A:

Q: Consider a rectangle with a measured width of ? = 9.6 ± 0.3 cm and a length of ? = 30.2 ± 0.7 cm.…

A:

Q: A typical human cell is approximately 12.00 μm in diameter and enclosed by a membrane that is 9.000…

A: Given:-  A typical human cell has an approximate in diameter of d= 12.00 μm The thickness of the…

Q: Kinetic energy K has dimensions kg ·m2/s2. It can be written in terms of the momentum p and mass m…

A: Given : (a) Kinetic energy K has dimensions kg ·m2/s2. K = p2/2m To determine: the proper units for…

Q: A model for the surface area of some solid object is given by S = 0.141w0.797 0.466, where w is the…

A:

Q: Express this product in units of km3 in standard scientific notation and with the appropriate number…

A: given that (4.2 km) × (4.0 m) × (13.24 × 10−3 mm)

Q: The period of oscillation of a simple pendulum is given by the equation T = k(L/ g)^1/2 where T is…

A: T=kLgT2=k2Lg

Q: В Consider the following equation: x= At² + (v+a) time and v is the speed. Find the dimensions of B:…

A:

Q: The active area of the processor found in some smartphones has the equivalent of about 2.0 billion…

A: Given : Number of transistors , N = 2 Billion = 2× 109  Dimensions of Integrated circuit = 9.3 mm ×…

Q: builder wants to install wall-to-wall carpeting in a living room of length 8.81 m and width 6.3 m.…

A: Given: Length of the room,  L=8.81 m Breadth of the room, b=6.3 m

Q: The Drake equation is a tool used by scientists engaged in the Search for Extraterrestrial…

A: The Drake equation is N=R×fS×nP×fL×fi×fT×L                                                       -…

Q: A round coin has a diameter of 19.55 mm, a thickness of 1.55 mm, and a mass of 2.50 g. What is its…

A:

Q: A rectangle has a length of (2.3 ± 0.1) m and a width of (1.4 ± 0.2) m. Calculate the area and the…

A:

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: 3. A physicist needs to estimate the density of a cube (all sides of the cube have equal length).…

A: The density is given byD=M/L3the data given, the massμM=1σM=0.02the mean value of length and…

Q: The period T of a simple pendulum is the amount of time required for it to undergo one complete…

A: The  expression for the time period of a simple pendulum is given,  T=2πLpgq

Q: 5. A certain brand of house paint claims coverage of 460ft^2/gal. what of the is the original…

A: Inverse of the original quantity is 2.17391 × 10-3 gal/ft2 Thickness is the ratio of volume per area…

Q: В. The atmospheric pressure P decreases exponentially with elevation h as follows, P(h) = P,e-gh/A…

A: The atmospheric pressure decreases exponentially with elevation as : P(h) = Poe-ghA

Scalars and Vectors

Scalars and Vectors are the classification of physical quantities that are used to denote various terms in physics.