Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Physics-

General

Easy

Question

Consider a particle moving without friction on a rippled surface, as shown. Gravity acts down in the negative h direction. The elevation h(x) of the surface is given by h(x) = d cos(kx). If the particle starts at x = 0 with a speed v in the x direction, for what values of v will the particle stay on the surface at all times?

$v \leq \sqrt{g d}$
$v \leq \sqrt{\frac{g}{k}}$
$v \leq \sqrt{g k d^{2}}$
$v \leq \sqrt{\frac{g}{k^{2} d}}$

The correct answer is: $v less or equal than square root of fraction numerator g over denominator k to the power of 2 end exponent d end fraction end root$

$table row cell R subscript C end subscript equals fraction numerator open parentheses 1 plus fraction numerator d y over denominator d x end fraction close parentheses to the power of 3 divided by 2 end exponent over denominator d to the power of 2 end exponent y divided by x to the power of 2 end exponent end fraction comma blank h e r e blank R subscript C end subscript blank a t blank x equals 0 equals fraction numerator 1 over denominator k to the power of 2 end exponent d end fraction end cell row cell therefore v less or equal than square root of g R subscript C end subscript end root equals square root of fraction numerator g over denominator k to the power of 2 end exponent d end fraction end root end cell end table$

Related Questions to study

System shown in figure is released from rest. Pulley and spring is massless and friction is absent everywhere. The speed of 5 kg block when 2 kg block leaves the contact with ground is (Take force constant of spring $open k equals 40 N divided by m blank a n d blank g equals 10 m divided by s to the power of 2 end exponent close parentheses$

System shown in figure is released from rest. Pulley and spring is massless and friction is absent everywhere. The speed of 5 kg block when 2 kg block leaves the contact with ground is (Take force constant of spring $open k equals 40 N divided by m blank a n d blank g equals 10 m divided by s to the power of 2 end exponent close parentheses$

physics-General

A smooth track in the form of a quarter circle of radius 6 m lies in the vertical plane. A particle moves from $P subscript 1 end subscript blank t o blank P subscript 2 end subscript$ under the action of forces $stack F with rightwards arrow on top subscript 1 end subscript comma stack F with rightwards arrow on top subscript 2 end subscript blank a n d blank stack F with rightwards arrow on top subscript 3 end subscript. blank F o r c e blank stack F with rightwards arrow on top subscript 1 end subscript$ is always toward $P subscript 2 end subscript$ and is always 20 N in magnitude. Force $stack F with rightwards arrow on top subscript 2 end subscript$ always acts horizontally and is always 30 N in magnitude. Force $stack F with rightwards arrow on top subscript 3 end subscript$ always acts tangentially to the track and is of magnitude 15 N. Select the correct alternative(s)

A smooth track in the form of a quarter circle of radius 6 m lies in the vertical plane. A particle moves from $P subscript 1 end subscript blank t o blank P subscript 2 end subscript$ under the action of forces $stack F with rightwards arrow on top subscript 1 end subscript comma stack F with rightwards arrow on top subscript 2 end subscript blank a n d blank stack F with rightwards arrow on top subscript 3 end subscript. blank F o r c e blank stack F with rightwards arrow on top subscript 1 end subscript$ is always toward $P subscript 2 end subscript$ and is always 20 N in magnitude. Force $stack F with rightwards arrow on top subscript 2 end subscript$ always acts horizontally and is always 30 N in magnitude. Force $stack F with rightwards arrow on top subscript 3 end subscript$ always acts tangentially to the track and is of magnitude 15 N. Select the correct alternative(s)

physics-General

Ball I is thrown towards a tower at an angle of 60° with the horizontal with unknown speed (u). At the same moment ball II is released from the top of tower as shown. Balls collide after two seconds and at the moment of collision, velocity of ball I is horizontal. Find

Ball I is thrown towards a tower at an angle of 60° with the horizontal with unknown speed (u). At the same moment ball II is released from the top of tower as shown. Balls collide after two seconds and at the moment of collision, velocity of ball I is horizontal. Find

physics-General

parallel

A ball of mass ‘m’ is rotating in a circle of radius ‘r’ with speed v inside a smooth cone as shown in figure. Let N be the normal reaction on the ball by the cone, then choose the wrong option.

A ball of mass ‘m’ is rotating in a circle of radius ‘r’ with speed v inside a smooth cone as shown in figure. Let N be the normal reaction on the ball by the cone, then choose the wrong option.

physics-General

System shown in the figure is released from rest when spring is unstretched. Pulley and spring is massless and friction is absent everywhere. The speed of 5 kg block when 2 kg block leaves the contact with ground is (Take force constant of spring k = 40 N/m and $open g equals 10 m divided by s to the power of 2 end exponent close parentheses$

System shown in the figure is released from rest when spring is unstretched. Pulley and spring is massless and friction is absent everywhere. The speed of 5 kg block when 2 kg block leaves the contact with ground is (Take force constant of spring k = 40 N/m and $open g equals 10 m divided by s to the power of 2 end exponent close parentheses$

physics-General

Two blocks of masses $m subscript 1 end subscript equals 1 k g blank a n d blank m subscript 2 end subscript equals 2 k g$ are connected by a non - deformed light spring. They are lying on a rough horizontal surface. The coefficient of friction between the blocks and the surface is 0.4. What minimum constant force F has to be applied in horizontal direction to the block of mass m1 in order to shift the other block? $open parentheses g equals 10 m divided by s to the power of 2 end exponent close parentheses$

Two blocks of masses $m subscript 1 end subscript equals 1 k g blank a n d blank m subscript 2 end subscript equals 2 k g$ are connected by a non - deformed light spring. They are lying on a rough horizontal surface. The coefficient of friction between the blocks and the surface is 0.4. What minimum constant force F has to be applied in horizontal direction to the block of mass m1 in order to shift the other block? $open parentheses g equals 10 m divided by s to the power of 2 end exponent close parentheses$

physics-General

parallel

In the figure shown the spring constant is K. The mass of the upper disc is m and that of the lower disc is 3m. The upper block is depressed down from its equilibrium position by a distance $delta$ =5mg/K and released at t=0. Find the velocity of ‘m’ when normal reaction on 3m is mg

In the figure shown the spring constant is K. The mass of the upper disc is m and that of the lower disc is 3m. The upper block is depressed down from its equilibrium position by a distance $delta$ =5mg/K and released at t=0. Find the velocity of ‘m’ when normal reaction on 3m is mg

physics-General

A block of mass 'm' is released from rest at point A. The compression in spring, when the speed of block is maximum

A block of mass 'm' is released from rest at point A. The compression in spring, when the speed of block is maximum

physics-General

A uniform rod of length l and mass m is allowed to rotate in a horizontal plane about a vertical axis OO¢ passing through one of its ends with an angular velocity $omega$ . Then the tension in the rod in terms of distance x measured from the axis of rotation is:

A uniform rod of length l and mass m is allowed to rotate in a horizontal plane about a vertical axis OO¢ passing through one of its ends with an angular velocity $omega$ . Then the tension in the rod in terms of distance x measured from the axis of rotation is:

physics-General

parallel

A particle P of mass m is attached to a vertical axis by two strings AP and BP of length l each. The separation AB=l. P rotates around the axis with an angular velocity $omega$ . The tensions in the two strings are $T subscript 1 end subscript blank a n d blank T subscript 2 end subscript$

A particle P of mass m is attached to a vertical axis by two strings AP and BP of length l each. The separation AB=l. P rotates around the axis with an angular velocity $omega$ . The tensions in the two strings are $T subscript 1 end subscript blank a n d blank T subscript 2 end subscript$

physics-General

A single wire ACB passes through a smooth ring at C which revolves at a constant speed in the horizontal circle of radius r as shown in the fig. The speed of revolution is

A single wire ACB passes through a smooth ring at C which revolves at a constant speed in the horizontal circle of radius r as shown in the fig. The speed of revolution is

physics-General

A body is thrown with a velocity of 10 m/s at an angle of 45° to the horizontal. The radius of curvature of its trajectory in $t equals 1 divided by square root of 2$ sec after the body began to move is :

A body is thrown with a velocity of 10 m/s at an angle of 45° to the horizontal. The radius of curvature of its trajectory in $t equals 1 divided by square root of 2$ sec after the body began to move is :

physics-General

parallel

Two identical blocks of weight W are placed one on top of the other shown in figure. The upper block is tied to the wall. The coefficient of static friction between B and ground is $mu$ and friction between A and B is absent when F = mw force is applied on the lower block as shown. The tension in the string will be

Two identical blocks of weight W are placed one on top of the other shown in figure. The upper block is tied to the wall. The coefficient of static friction between B and ground is $mu$ and friction between A and B is absent when F = mw force is applied on the lower block as shown. The tension in the string will be

physics-General

Block A is placed on cart B as shown id figure. If the coefficients of static and kinetic friction between the 20 kg block A and 100 kg cart B are both essentially the same value of 0.5 $open square brackets g equals 10 m divided by s to the power of 2 end exponent close square brackets$

Block A is placed on cart B as shown id figure. If the coefficients of static and kinetic friction between the 20 kg block A and 100 kg cart B are both essentially the same value of 0.5 $open square brackets g equals 10 m divided by s to the power of 2 end exponent close square brackets$

physics-General

For the two blocks initially at rest under constant ext. forces of mass1 kg and 2kg shown, $a subscript 1 end subscript equals 5 m divided by s to the power of 2 end exponent rightwards arrow comma a subscript 2 end subscript equals 2 m divided by s to the power of 2 end exponent leftwards arrow$ Which of the following is correct?

For the two blocks initially at rest under constant ext. forces of mass1 kg and 2kg shown, $a subscript 1 end subscript equals 5 m divided by s to the power of 2 end exponent rightwards arrow comma a subscript 2 end subscript equals 2 m divided by s to the power of 2 end exponent leftwards arrow$ Which of the following is correct?

physics-General

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.