Published by:
CGP EDU Academic Team
Published on: September 12, 2026
A force
acts at a point
. Then the magnitude of torque aboutthe point
will be
. The value of
is :
Text Solution
Verified by ExpertsThe correct answer is:
C
Step 1: Understand the torque formula. Torque (D) is given by the formula:
D = r imes F
where r is the position vector from the point about which we are calculating the torque to the point where the force is applied, and F is the force vector.
Step 2: Define the vectors based on the figures provided.
Force vector: F = (1i + 2j + 3k) N.
Position vector from point C (where torque is calculated) to point A (where force is applied): r = (4i + 3j - 3k) m - (1i + 2j + 1k) m = (3i + j - 4k) m.
Step 3: Calculate the cross product r imes F:
r = (3i + 1j - 4k) and F = (1i + 2j + 3k).
Using the determinant method for the cross product:
|i j k|
|3 1 -4|
|1 2 3|
Calculating the determinant gives us:
Torque = i(-2 - -12) - j(9 - -4) + k(6 - 3) = 10i - 13j + 3k.
Step 4: Find the magnitude of the torque vector:
|T| = √(10^2 + (-13)^2 + 3^2) = √(100 + 169 + 9) = √278.
As we need to express the magnitude in the provided format, it simplifies to sqrt(x) N - m where x = 278. Thus the correct choice is C.
D = r imes F
where r is the position vector from the point about which we are calculating the torque to the point where the force is applied, and F is the force vector.
Step 2: Define the vectors based on the figures provided.
Force vector: F = (1i + 2j + 3k) N.
Position vector from point C (where torque is calculated) to point A (where force is applied): r = (4i + 3j - 3k) m - (1i + 2j + 1k) m = (3i + j - 4k) m.
Step 3: Calculate the cross product r imes F:
r = (3i + 1j - 4k) and F = (1i + 2j + 3k).
Using the determinant method for the cross product:
|i j k|
|3 1 -4|
|1 2 3|
Calculating the determinant gives us:
Torque = i(-2 - -12) - j(9 - -4) + k(6 - 3) = 10i - 13j + 3k.
Step 4: Find the magnitude of the torque vector:
|T| = √(10^2 + (-13)^2 + 3^2) = √(100 + 169 + 9) = √278.
As we need to express the magnitude in the provided format, it simplifies to sqrt(x) N - m where x = 278. Thus the correct choice is C.
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