Which of the following is the correct unit af
gravitational potential?? (A) jkg^-2 (B) Nkg^-1(C)Jkg^3 (D)J kg-1
7 answers
The correct unit for gravitational potential is (D) J kg-1.
Determine the vector product of D = 5i-6j-3k and E=71+8j+4k.
To find the vector product (also known as the cross product) of two vectors, we use the formula:
D × E = (DyEz - DzEy)i - (DxEz - DzEx)j + (DxEy - DyEx)k
Given:
D = 5i - 6j - 3k
E = 7i + 8j + 4k
Let's substitute the values into the formula:
D × E = ((-6) * 4 - (-3) * 8)i - (5 * 4 - (-3) * 7)j + (5 * 8 - (-6) * 7)k
= (-24 + 24)i - (20 + 21)j + (40 + 42)k
= 0i - 41j + 82k
Therefore, the vector product of D and E is 0i - 41j + 82k.
D × E = (DyEz - DzEy)i - (DxEz - DzEx)j + (DxEy - DyEx)k
Given:
D = 5i - 6j - 3k
E = 7i + 8j + 4k
Let's substitute the values into the formula:
D × E = ((-6) * 4 - (-3) * 8)i - (5 * 4 - (-3) * 7)j + (5 * 8 - (-6) * 7)k
= (-24 + 24)i - (20 + 21)j + (40 + 42)k
= 0i - 41j + 82k
Therefore, the vector product of D and E is 0i - 41j + 82k.
A particle nt position r= i+ 2j+ 3k is acted
upon by a force F= 4i+ 5j + 6k.Calculate the
toque experienced by the particle.
upon by a force F= 4i+ 5j + 6k.Calculate the
toque experienced by the particle.
To calculate the torque experienced by the particle, we need to find the cross product of the position vector (r) and force vector (F). The torque vector (τ) can be calculated using the formula:
τ = r × F
Given:
r = i + 2j + 3k
F = 4i + 5j + 6k
Let's substitute the values into the formula:
τ = ((2 * 6) - (3 * 5))i - ((1 * 6) - (3 * 4))j + ((1 * 5) - (2 * 4))k
= (12 - 15)i - (6 - 12)j + (5 - 8)k
= -3i + 6j - 3k
Therefore, the torque experienced by the particle is -3i + 6j - 3k.
τ = r × F
Given:
r = i + 2j + 3k
F = 4i + 5j + 6k
Let's substitute the values into the formula:
τ = ((2 * 6) - (3 * 5))i - ((1 * 6) - (3 * 4))j + ((1 * 5) - (2 * 4))k
= (12 - 15)i - (6 - 12)j + (5 - 8)k
= -3i + 6j - 3k
Therefore, the torque experienced by the particle is -3i + 6j - 3k.
A particle nt position r=i+ 2j+ 3k is acted
upon by a force F= 4i+5j+6k. Calculate the
toque experienced by the particle.
upon by a force F= 4i+5j+6k. Calculate the
toque experienced by the particle.
To calculate the torque experienced by the particle, we need to find the cross product of the position vector (r) and force vector (F). The torque vector (τ) can be calculated using the formula:
τ = r × F
Given:
r = i + 2j + 3k
F = 4i + 5j + 6k
Let's substitute the values into the formula:
τ = (2 * 6 - 3 * 5)i - (1 * 6 - 3 * 4)j + (1 * 5 - 2 * 4)k
= (12 - 15)i - (6 - 12)j + (5 - 8)k
= -3i + 6j - 3k
Therefore, the torque experienced by the particle is -3i + 6j - 3k.
τ = r × F
Given:
r = i + 2j + 3k
F = 4i + 5j + 6k
Let's substitute the values into the formula:
τ = (2 * 6 - 3 * 5)i - (1 * 6 - 3 * 4)j + (1 * 5 - 2 * 4)k
= (12 - 15)i - (6 - 12)j + (5 - 8)k
= -3i + 6j - 3k
Therefore, the torque experienced by the particle is -3i + 6j - 3k.