If a force $10 \widehat i +15 \widehat j + 25 \widehat k$ acts on a system and gives an acceleration $2 \widehat i + 3 \widehat j - 5 \widehat k$ to the centre of mass of the system, the mass of the system is
If a force $10 \widehat i +15 \widehat j + 25 \widehat k$ acts on a system and gives an acceleration $2 \widehat i + 3 \widehat j - 5 \widehat k$ to the centre of mass of the system, the mass of the system is
- A
$5 \,units$
- B
$\sqrt {38} \,units$
- C
$5 \sqrt {38} \,units$
- D
given data is not correct
Similar Questions
Explain the theoretical method for estimation of the centre of mass of a solid body.
Explain the theoretical method for estimation of the centre of mass of a solid body.
A rod of length $3\, m$ and its mass per unit length is directly proportional to the distance $x$ from its one end. The center of gravity of the rod from that end will be at ........ $ m$
A rod of length $3\, m$ and its mass per unit length is directly proportional to the distance $x$ from its one end. The center of gravity of the rod from that end will be at ........ $ m$
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$(a)$ Centre of gravity $(C.G.)$ of a body is the point at which the weight of the body acts.
$(b)$ Centre of mass coincides with the centre of gravity if the earth is assumed to have infinitely large radius
$(c)$ To evaluate the gravitational field intensity due to any body at an external point, the entire mass of the body can be considered to be concentrated at its $C.G.$
$(d)$ The radius of gyration of any body rotating about an axis is the length of the perpendicular dropped from the $C.G.$ of the body to the axis of rotation.
Which one of the following pairs of statements is correct ?
$(a)$ Centre of gravity $(C.G.)$ of a body is the point at which the weight of the body acts.
$(b)$ Centre of mass coincides with the centre of gravity if the earth is assumed to have infinitely large radius
$(c)$ To evaluate the gravitational field intensity due to any body at an external point, the entire mass of the body can be considered to be concentrated at its $C.G.$
$(d)$ The radius of gyration of any body rotating about an axis is the length of the perpendicular dropped from the $C.G.$ of the body to the axis of rotation.
Which one of the following pairs of statements is correct ?
- [AIPMT 2010]
A wheel in uniform motion about an axis passing through its centre and perpendicular to its plane is considered to be in mechanical (translational plus rotational) equilibrium because no net external force or torque is required to sustain its motion. However, the particles that constitute the wheel do experience a centripetal the acceleration directed towards the centre. How do you reconcile this fact with the wheel being in equilibrium?
How would you set a half wheel into uniform motion about an axis passing through the centre of mass of the wheel and perpendicular to its plane? Will you require external forces to sustain the motion ?
A wheel in uniform motion about an axis passing through its centre and perpendicular to its plane is considered to be in mechanical (translational plus rotational) equilibrium because no net external force or torque is required to sustain its motion. However, the particles that constitute the wheel do experience a centripetal the acceleration directed towards the centre. How do you reconcile this fact with the wheel being in equilibrium?
How would you set a half wheel into uniform motion about an axis passing through the centre of mass of the wheel and perpendicular to its plane? Will you require external forces to sustain the motion ?