Advertisements
Advertisements
Question
A block A can slide on a frictionless incline of angle θ and length l, kept inside an elevator going up with uniform velocity v in the following figure. Find the time taken by the block to slide down the length of the incline if it is released from the top of the incline.
Advertisements
Solution
The force on the block which makes the body move down the plane is the component of its weight parallel to the inclined surface.
F = mg sinθ
Acceleration, g = sin θ
Initial velocity of block, u = 0
Distance to be covered
s = l
a = g sin θ
Using, \[s = ut + \frac{1}{2}a t^2\]
\[l = 0 + \frac{1}{2}\left( g\sin\theta \right) t^2 \]
\[ \Rightarrow t^2 = \frac{2l}{g\sin\theta}\]
\[ \Rightarrow \text{ Time taken }, t ={\sqrt{\frac{2l}{gsin\theta}}}\]
APPEARS IN
RELATED QUESTIONS
A rocket with a lift-off mass 20,000 kg is blasted upwards with an initial acceleration of 5.0 m s–2. Calculate the initial thrust (force) of the blast.
An object is placed far away from all the objects that can exert force on it. A frame of reference is constructed by taking the origin and axes fixed in this object. Will the frame be necessarily inertial?
When a horse pulls a cart, the force that helps the horse to move forward is the force exerted by
A smooth wedge A is fitted in a chamber hanging from a fixed ceiling near the earth's surface. A block B placed at the top of the wedge takes time T to slide down the length of the wedge. If the block is placed at the top of the wedge and the cable supporting the chamber is broken at the same instant, the block will.
In a TV picture tube, electrons are ejected from the cathode with negligible speed and they attain a velocity of 5 × 106 m/s in travelling one centimetre. Assuming straight-line motion, find the constant force exerted on the electrons. The mass of an electron is 9.1 × 10−31 kg.
Two blocks of equal mass m are tied to each other through a light string. One of the blocks is pulled along the line joining them with a constant force F. Find the tension in the string joining the blocks.
Consider the situation shown in the following figure All the surfaces are frictionless and the string and the pulley are light. Find the magnitude of acceleration of the two blocks.
Consider the situation shown in the following figure. Both the pulleys and the string are light and all the surfaces are frictionless.
- Find the acceleration of the mass M.
- Find the tension in the string.
- Calculate the force exerted by the clamp on the pulley A in the figure.
A monkey is climbing on a rope that goes over a smooth light pulley and supports a block of equal mass at the other end in the following figure. Show that whatever force the monkey exerts on the rope, the monkey and the block move in the same direction with equal acceleration. If initially both were at rest, their separation will not change as time passes.
A body of mass m moving with a velocity v is acted upon by a force. Write an expression for change in momentum in each of the following cases: (i) When v << c, (ii) When v → c and (iii) When v << c but m does not remain constant. Here, c is the speed of light.
State the Newton's second law of motion. What information do you get from it?
The linear momentum of a body of mass m moving with velocity v is :
A ball is thrown vertically upwards. It returns 6 s later. Calculate the greatest height reached by the ball. (Take g = 10 m s−2)
A pebble is dropped freely in a well from its top. It takes 20 s for the pebble to reach the water surface in the well. Taking g = 10 m s-2 and speed of sound = 330 m s-1. Find : The depth of water surface
ame the law of motion which gives the definition of force.
What causes motion in a body?
A ball is thrown vertically downward with an initial velocity of 10 m/s. What is its speed 1 s later and 2 s later?
