a wheel having diameter 2m starts from rest and accelerates uniformly to an angular velocity of 75 revoulutions per minute in 5s. calculate its angular acceleration?
Q;- one of the rectangular components of velocity of 80km/hr find other component?
Q:-the diameter of sphere is 5.32cm. calculate its surface area with due regard to significant figures as in diameter?
Q:-the maximum error in the measurement of mass and length of a cube are 3% and 2% respectively. what will be the max error in measurement of density?
Q;-the wave length (d) associated with a moving particle depends upon it mass (m) velocity (v) and plan k's contant (h). find a relation between them by using principle of homogencity?
Q:- write the dimensional formula of following physical quantities?
1. Solidangle
2. Stress
3.Thermal conductivity
4.Refrective index
5. Homent of inertia.
Q:-Find no. of watts in one horse power watts is unit of power on the MKS system and horse power that of powes in FPS system.
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To solve the questions, let's go through each one step by step:
Q1: To calculate the angular acceleration, we can use the formula:
Angular acceleration (α) = (Final angular velocity - Initial angular velocity) / Time
Given:
Initial angular velocity (ω1) = 0 rev/s
Final angular velocity (ω2) = 75 rev/min
Time (t) = 5 s
We need to convert the final angular velocity from rev/min to rev/s:
75 rev/min * (1 min/60 s) = 1.25 rev/s
Now we can calculate the angular acceleration:
α = (1.25 rev/s - 0 rev/s) / 5 s
α = 1.25 rev/s / 5 s
α = 0.25 rev/s²
Therefore, the angular acceleration is 0.25 rev/s².
Q2: When a velocity vector is given in rectangular components, we can find the other component using vector components.
Given:
One rectangular component of velocity = 80 km/hr
Let's assume the given component is in the x-direction (Vx) and we need to find the other component in the y-direction (Vy).
We can use the Pythagorean theorem to find the magnitude of the total velocity:
V (magnitude) = √(Vx² + Vy²)
Since we only have one component, we can rearrange the equation:
V (magnitude) = √(Vx² + 0²)
V (magnitude) = Vx
Therefore, the other component in the y-direction is 0 km/hr.
Q3: To calculate the surface area of a sphere with respect to significant figures, we need to consider the significant figures in the diameter.
Given:
Diameter (d) = 5.32 cm
The surface area (A) of a sphere is given by the formula:
A = 4πr²
We need to use the diameter to find the radius (r):
r = d/2
r = 5.32 cm / 2
r = 2.66 cm
Now we can calculate the surface area:
A = 4π(2.66 cm)²
Make sure to use the appropriate value of π according to the number of significant figures required. Finally, round the answer to the appropriate number of significant figures based on the given diameter.
Q4: To find the maximum error in the measurement of density, we need to consider the percentage errors in the mass and length measurements.
Given:
Percentage error in mass = 3%
Percentage error in length = 2%
The formula for density (ρ) is:
ρ = mass / volume
The volume (V) of a cube can be expressed as V = length³.
Using the formula for percentage error, we can calculate the maximum error in density:
Maximum error in density (Δρ) = (Percentage error in mass + 3 * Percentage error in length) * ρ
Make sure to convert the percentage errors to decimal form (e.g., 3% = 0.03) before calculating the maximum error.
Q5: According to the principle of homogeneity, the dimensions on both sides of an equation should be the same.
Given:
Wavelength (λ) depends on mass (m), velocity (v), and Planck's constant (h)
The dimensional formula for wavelength can be expressed as:
[λ] = [m^a * v^b * h^c]
To find the relation between them, we need to determine the values of exponents (a, b, c) using the principle of homogeneity. We can equate the dimensions of both sides of the equation and solve for the exponents.
Q6: Dimensional formulas for the given physical quantities:
1. Solid angle: It is a dimensionless quantity. Therefore, the dimensional formula is [Solid angle] = 1.
2. Stress: The dimensional formula for stress is:
[Stress] = [Force] / [Area]
= [M L T^(-2)] / [L^2]
= [M L^(-1) T^(-2)]
3. Thermal conductivity:
[Thermal conductivity] = [Heat energy] / [Length * Time * Temperature difference]
= [M L T^(-3) θ^(-1)]
4. Refractive index: It is a dimensionless quantity. Therefore, the dimensional formula is [Refractive index] = 1.
5. Moment of inertia:
[Moment of inertia] = [Mass] * [Length]^2
= [M L^2]
Q7: Horsepower is a unit of power in the FPS (foot-pound-second) system, while the watt is a unit of power in the MKS (meter-kilogram-second) system.
The conversion relation between horsepower and watts is:
1 horsepower = 745.7 watts.
So, there are 745.7 watts in one horsepower.