#### A train passes over a 400 m long bridge. If the speed of the train is 30 m/s and the train takes 20 s to cross the bridge, then the length of the train is ____ m.

Distance travelled by the train, S = vt ⇒ S = 30 × 20 ∴ S = 600 Total length covered by the train = length of the train + length of the bridge ⇒ 600 = 400 + length of the train Hence, the length of the train is 200 m.

#### A labour carrying a suitcase on his head moves from rest on a horizontal road to another point and finally comes to rest. Then, the work done by gravity is ____.

As, W = FScosθ As the angle between the force applied by gravity and displacement, θ = 90° Hence, work done is zero.

#### The velocity-time graph of a body with uniform velocity is a straight line ____.

When we say that body is moving with uniform velocity it means there is no acceleration. The slope of the velocity-time graph has zero degree inclination to the X-axis i.e., tanθ = tan0° = 0. Hence, the acceleration is zero and the velocity-time graph is parallel to the X-axis.

#### An object can be at rest as well as in motion at the same time.

An object can be at rest relative to one object as well as in motion at the same time relative to another object.

#### The velocity-time graph for a body with non-uniform motion having constant acceleration is a ____.

The velocity-time graph for a body with non-uniform motion having constant acceleration is a straight line inclined to the time axis.

#### Work is measured as a product of ____.

Work done is given by the product of force and displacement, represented by, Work = force × displacement.

#### Work done in raising a box on to a platform depends on ____.

Work done in raising a box on to a platform depends on the height to which it is raised. When a body is raised to a height then work done is equal to the potential energy.

#### In the equation of motion, x = at + bt^{2}, the units of a and b are ____ respectively.

As, L.H.S. and R.H.S of the equation, x = at + bt^{2}, has same physical unit. Since, ‘x’ represents the distance in the given equation then 'at' and ' bt^{2}' must have same unit i.e., metre. ⇒ Unit of at is metre ∴ Unit of 'a' is m/s and 'b' is m/s^{2}.

#### Which of the following is a wrong statement regarding the graphical representation of motion of an object?

By representing the motion of an object graphically, we can: Infer the nature of motion Determine its position at any intermediate interval. Calculate its acceleration, displacement, velocity, etc. at any instant and Derive equations of motion

#### Work done by a centripetal force ____.

Work done, W = FScosθ Centripetal force is always perpendicular to the direction of displacement. θ = 90°, cos90° = 0. Hence, work done by the centripetal force is always zero.

#### No work is said to be done, when an object moves at an angle of ____ with the direction of the force.

Given, W = 0 Work done is given by, W = FScosθ cosθ = 0; θ = 90° Hence, work done is zero.

#### A girl lifts a doll from the floor and places it on a table. If the weight of the doll is known, then ____ is required to calculate the work done by the girl on the doll.

Given, force, F = mg; Work done is given by the girl, W = FScosθ to find the work done by the girl, displacement is required. The doll is moved from the ground to the top of table. Hence, the height of the table is required to find the work done by the girl on the doll.

#### When a body is whirled in a circle, then work done on it by the tension in the string is ____.

Work done is given by, W = FScosθ As, θ = 90° and cos90° = 0 Hence, work done by the tension in the string is zero.

#### A body moving along a circular track of radius R completes one rotation in 2 seconds. Its average velocity in 2 second is ____ m/s.

The body completes one rotation in 2 second, so its displacement in 2 seconds is 0 m. Hence, the average velocity of the body in 2 seconds is 0 m/s.

#### When the force applied and the displacement of the body is inclined at 90°, with each other, the work done is ____.

Work done = FScosθ As, cos90° = 0 Therefore, work done is zero.

#### A body in uniform circular motion has ____.

In uniform circular motion, the magnitude of velocity of the particle is constant, but its direction changes with time. Hence, a body in uniform circular motion has constant speed.

#### Work done by the electrostatic force on an electron revolving around the nucleus of hydrogen is ____ J.

The electrostatic force and displacement of an electron are mutually perpendicular to each other. Hence, the work done by the electrostatic force on an electron revolving around the nucleus of hydrogen is zero.

#### If the displacement-time graph of a particle represents a line parallel to the time-axis, then the velocity of the particle is ____.

The inclination of the displacement-time graph with time axis gives the magnitude of velocity. As the graph representing a line parallel to the time-axis, the velocity of the particle is zero.

#### A body in motion comes to rest when force is applied on it. The work done by the force on the body is ____.

Force and displacements are in opposite direction. A body in motion comes to rest when force is applied on it. Hence, the work done by the force on the body is negative.

#### A body moving with uniform acceleration 2 m/s^{2} covers a distance of 150 m in10 seconds. Then, the initial velocity of the body is ____ m/s.

Let 'u' be the initial velocity and 'a' be the acceleration. Then, ⇒ 150 = 10 u + 12 × 2 × 100 ⇒ 15 = u + 10 ∴ u = 5 m/s Therefore, the initial velocity of the body is 5 m/s.

#### The unit Nm is equivalent to ____.

Unit Nm is equivalent to J.

#### Area under a velocity-time graph gives the ____ of the body.

Area under a velocity-time graph gives displacement of the body.

#### kg m^{2}/s^{2} represents the unit of ____.

Work done, W = FScosθ SI unit of work is N m (or) kg m^{2}/s^{2} and torque = r × F SI unit of torque is N m (or) kg m^{2}/s^{2} Hence, work done and torque have same unit.

#### Work done by the gravitational force on a body is ____.

When a body is carried along the direction of the gravitational force, the work done is positive and vice-versa. When the displacement is made perpendicular to the direction of the gravitational force, the work done is zero.

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