solve Q 7 plz dont give link

solve Q 7 plz dont give link e power delivered to the particle during the first half ot tn e radius of curvature of the trajectory of the particle at the highest point Of the projectile is 7.5m. 6. A particle is shifted from A to B and then from B to C where A, B and C are the midpoints of the corresponding faces of a cube of side 2m. If a force É = (3i + 4j — 510 N is continuously acting on the particle, then select correct alternative v"ork done from A to B is 7 J ;work done from B to C is I J done A to C is 8 J É is a conservative force 7. 8. Which of the following is/are conservative force(s)? 3(yi+ x j) If one of the forces acting on a particle is conservative then : g Work done by this force is zero when the particle moves exactly once around any closed path' (B) Work done by this force equals the change in the kinetic energy of the particle. tceflt obeys Newton's second law. L(DfWork done by this force depends on the end points of the motion, not on the path in between• A Darticle of mass m = I kg lying on x—axis experiences a force given

Dear Student,

The force will be conservative if curl of Force field is zero.
i.e. ∇ x F = 0.

If F = F_xi + F_y j + F_Z k , than , ∇ x F =

|\begin{matrix} i & j & k \\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\ F_{x} & F_{y} & F_{z} \end{matrix}|

i [\frac{\partial}{\partial y} (F_{z}) - \frac{\partial}{\partial z} (F_{y})] - j [\frac{\partial}{\partial x} (F_{z}) - \frac{\partial}{\partial z} (F_{x})] + k [\frac{\partial}{\partial x} (F_{y}) - \frac{\partial}{\partial y} (F_{x})]

.......(1)

Now we will solve all the four options one by one using equation (1).,

(a).

F = 2 r^{3} r = 2 r^{2} \vec{r} = 2 (x^{2} + y^{2} + z^{2}) (x i + yj + zk)) . [position vector, \vec{r} = (xi + yj + zk) And |r| = (x^{2} + y^{2} + z^{2})^{\frac{1}{2}} . Now using (1), \nabla \times F = 0 .

So force F is conservative in nature.

similarly we can check for (b),(c) and (d).

and we will get, (b) and (c) also are conservative forces, but force given in (d) is not conservative.

Hence, (a),(b),(c) are conservative in nature and (d) is non- conservative in nature.

Regards..

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