Work-energy-power practice · Medium

The angular acceleration of a body, moving along the circumference of a circle, is

The potential energy of a particle of mass $1 \mathrm{~kg}$ is $U=10+(x-2)^2$. Here, $U$ is in joule and $x$ in metre on the positive $X$-axis. Particle travels upto $x=+6 \mathrm{~m}$. Choose the correct option.

Identify the correct statements from the following:

A. Work done by a man in lifting a bucket out of a well by means of rope tied to the bucket is negative.

B. Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative.

C. Work done by friction on a body sliding down an inclined plane is positive.

D. Word done by an applied force on a body moving on a rough horizontal plane with uniform velocity is zero.

E. Work done by the air resistance on an oscillating pendulum is negative.

Choose the correct answer from the options given below:

Potential energy function along $x$-axis in a certain force field is given as $U(x)=\frac{x^4}{4}-2 x^3+\frac{11}{2} x^2-6 x$. For the given force field,

(i) the points of equilibrium are $x=1, x=2$ and $x=3$

(ii) the points $x=2$ is a point of unstable equilibrium

(iii) the points $x=1$ and $x=3$ are points of stable equilibrium

(iv) there exists no point of neutral equilibrium Which one of the following is the set of correct options?

Which of the following statements is FALSE for a particle moving in a circle with a constant angular speed?

The potential energy function associated with the force $\vec{F}=4 x y \hat{i}+2 x^2 \hat{j}$ is

A point of application of a force $\mathrm{\vec F} = 5\hat i - 4\hat j + 2\hat k$ is moved from $\overrightarrow {{\mathrm{r}_1}} = 2\hat i + 7\hat j + 4\hat k\,to\,\overrightarrow {{\mathrm{r}_2}} = 5\hat i + 2\hat j + 3\hat k$ the work done is

The displacement x in metre of a particle of mass m kg moving in one dimension under the action of a force is related to the time t in second by the equation $t = \sqrt x + 3$, the work done by the force (in joule) in first six seconds is

Statement I: The tendency to overturn of skidding/overturning is quadrupled, when a cyclist doubles his speed of turning.

Statement II: $\tan \theta=\frac{\mathrm{v}^2}{\mathrm{Rg}} \Rightarrow$ becomes 4 times as $v$ doubled.

A small ball is dropped from a height of 10 m on horizontal floor. If the coefficient of restitution between ground and ball is 0.5 then maximum height to which ball will rise after second collision with ground is

Two masses of M and 4M are moving with equal kinetic energy. The ratio of their linear momentum is

A peculiar spring has a force law $F=-{d} x^3$ which of the following is true?

A cane filled with water is revolved in a vertical circle of radius 4 m and the water just does not fall down. The time period of revolution will be

Statement-I: The work done by all forces on a system equals to the change in kinetic energy of that system. This statement is true even if non-conservative forces act on the system.
Statement-II: The total work done by internal forces may be positive.

A body of mass 5 kg is placed at the origin, and can move only on the x-axis. A force of 10 N is acting on it in a direction making an angle of ${60^0}$ with the x-axis and displaces it along the x-axis by 4 metres. The work done by the force is

Work done by a frictional force is

A body moves from a position ${r_1} = \left( {2\hat i - 3\hat j - 4\hat k} \right)$ m to a position, ${r_2} = \left( {3\hat i - 43\hat j - 5\hat k} \right)$ m under the influence of a constant force $F = \left( {4\hat i - 4\hat j + 5\hat k} \right)$ N. The work done by the force is

You accidentally bump into a bookcase. It tilts briefly but then returns to upright, and you breathe a sigh of relief. When you first bumped the bookcase, its center of gravity moved

Which of the following quantities measured from different inertial reference frames are same?

For a particle in non-uniform accelerated circular motion

If F is the force required to keep a train moving at a constant speed v,the power required is

A sphere of mass M moving with velocity collides elastically with another of mass ‘m’ at rest. After collision their final velocities are ${V_1}\,\,and\,\,{V_2}$ then the value of $\,{V_2}$ is

For inelastic collision between two spherical rigid bodies

A light and a heavy body have equal momenta. Which one has greater K.E.

A body constrained to move in Y direction, is subjected to a force given by $\mathrm{\vec F} = \left( { - 2\hat i + 15\hat j + 6\hat k} \right)$ N done by this force in moving the body through a distance of 10m along Y axis?

When a body moves with a constant speed along a circle

A uniform chain of mass M and length L is lying on a frictionless table in such a way that its 1/3 part is hanging vertically down. The work done in pulling the chain up the table is

A ball of mass m moves with speed v and strikes a wall having infinite mass and it returns with same speed then the work done by the ball on the wall is

Which of the following statements is false for a particle moving in a circle with a constant angular speed?

Two students are sitting face to face, at two ends of a long compartment of a train, running at a constant acceleration. They toss a ball to each other, with the same muzzle velocity and at the same inclination to the vertical.
Statement-1: The time intervals for the free fall in either direction are equal.
Statement-2: In the frame of compartment velocity is changing but the vertical velocity remains unaffected by the horizontal acceleration of the cart.