help@askiitians.com

+91-87964 74404

Grade upto college level Mechanics

An object is moving with velocity given by where vz(t) = 0. From this, one can conclude
(a) that the acceleration
(A) will have no components that are identically zero.
(B) may have some componets that are identically zero.
(C) will have only a z component that is identically zero.
(D) will have an identically zero z component, and maybe an identically zero component in the x or y direction.
(b) and that the position
(A) will have no components that are identically zero.
(B) May have some components that are identically zero.
(C) Will have only a z component that is identically zero.
(D) Will have an identically zero z component, and maybe. An identically zero component in the x or y direction.

Amit Saxena

11 Years agoGrade upto college level

1 Answer

Deepak Patra

11 Years ago

(a)
The correct option is: (D) will have an identically zero z component, and maybe an identically zero component in x or y direction.
(b)
The correct option is: (D) will have an identically zero z component, and maybe an identically zero component in x or y direction
(a)
The acceleration of the object with velocity vector $\overrightarrow{v}(t) = v_{x}(t)\widehat{i} + v_{y}(t)\widehat{j} + v_{z}\widehat{k}$
is:

From this equation it is clear that the acceleration of the object depends on the change in magnitude of x component of velocity and y component of velocity respectively. Therefore the acceleration vector have an identically zero z component. Depending upon the values of v_x(t) and v_y (t), the x and y component of acceleration vector can also become zero.
However, if v_x (t) and v_y (t) are time dependent functions, x and y component of acceleration vector is guaranteed to be non-zero.
Therefore, the correct option is (D), and the rest are ruled out.
It is important to note that (C) comes closer to (D), but (C) rules out the probability that the acceleration vector can have zero x and y components.
(b)
It can be deduced from equations $\overrightarrow{a}(t) = \frac{d}{dt} v_{x}(t)\widehat{i}+ \frac{d}{dt}v_{y}(t)\widehat{j}$ and $\overrightarrow{v} (t) = v_{x} (t)\widehat{i}+v_{y}(t)\widehat{j}$ $(v_{z}(t)= 0)$ that the object move in the xy the plane, and its motion is restricted in two dimensions. Therefore there will be no z component in the position vector of the object, however there will be components of position vector in x and y directions respectively.
The object can also have identically zero x and y components of position vector (if the objects move along the axis), but this would ensure that either v_x (t) of or v_y (t) to be zero.
Therefore, the correct option is (D), and the rest are ruled out

Three identical balls are placed on a frictionless horizontal surface touching each other. They stick to each other because of adhesive. Another ball of same radius and mass m is placed over the void created by the three balls. Find the forces applied by the balls kept on the floor to each other if the system remains in equilibrium.

mechanics

1 Answer Available

Last Activity: 9 Months ago

A car loaded with water having total mass 1000 kg moves on a straight horizontal Road starting from rest under the action of a force of 100 Newton. The water spills throw a small hole in the bottom at a rate of 0.1 KG per second the velocity of cart after 300 seconds is nearly.

11
21
31
41

mechanics

1 Answer Available

Last Activity: 9 Months ago

A metal strip clamped at one end vibrates with a frequency of 20 Hz and amplitude of 5 mm
at the free end, where a small mass of 2 g is positioned. determine
(i) The velocity of the end when passing through the zero position
(ii) The acceleration at maximum displacement
(iii) The maximum kinetic energy of the mass

mechanics

2 Answers Available

Last Activity: 3 Years ago

An object of mass m = 0.25 kg oscillates in a fluid at the end of a vertical spring of spring
constant kH = 85 N/m, see Fig.1. The effect of the fluid resistance is governed by the
damping constant b = 0.07kg/s.
(i) Find the period of the damped oscillation.
(ii) By what percentage does the amplitude of the oscillation decrease in each cycle?

mechanics

1 Answer Available

Last Activity: 3 Years ago

If a=x² find the displacement at t =3sec if body velocity at t= 0 sec is 0

mechanics

1 Answer Available

Last Activity: 3 Years ago

View all Questions