Home
Class 12
PHYSICS
If the depth d to which a bullet of kine...

If the depth d to which a bullet of kinetic energy K can penetrate into a human body of modulus of electicity E, using the method of dimension, establish a relation between d, K and E . If `K=cd^(x) E^(y)`, fill x+y in OMR sheet. Modulus of elasticity =Force/Area ,`xx l/(Deltal)`

Text Solution

Verified by Experts

The correct Answer is:
`0004`

`K=cd^(x) E^(y)`
`ML^(2)T^(-2)=L^(X)[ML^(-1)T^(-2)]^(Y)`
`-2=-2y " " rArr y=1`
`2=x-y " " rArr x=3 " " x+y=4`
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

The depth x to which a bullet penetrates a human body depends on (i) coeffeicint of elasticity, eta and (ii) KE (E_k) of the bullet, By the method of dimensions, show that x prop ((E_k)/(eta))^(1//3)

The velocity of sound waves 'v' through a medium may be assumed to depend on : (i) the density of the medium 'd' and (ii) the modulus of elasticity 'E' . Deduce by the method of dimensions the formula for the velocity of sound . Take dimensional constant K=1.

The SI unit of energy is J = kg m^2 s^(-2), that of speed upsilon is ms^(-1) and of acceleration a is ms^(-2) which of the formulae for kinetic energy (K) given below can you rule out on the basis of dimensional arguments (m stands for the mass of the body). (a) K = m^2 upsilon^3 (b) K = (1)/(2)m upsilon^2 (c ) K= ma (d) K =(3)/(16)m upsilon^2 (e ) K = (1)/(2) m upsilon^2 +ma

For a body executing S.H.M. : (a) Potential energy is always equal to its K.E. (b) Average potential and kinetic energy over any given time inteval are always equal. (c ) Sum of the kinetic and potential energy at any point of time is constant. (d) Average K.E in one time period is equal to average potential energy in one time period . Choose the most approprate ooption from the options given below :

The time period of oscillation of a body is given by T=2pisqrt((mgA)/(K)) K: Represents the kinetic energy, m mass, g acceleration due to gravity and A is unknown If [A]=M^(x)L^(y)T^(z) , then what is the value of x+y+z?

The energy E of an oscillating body in simple harmonic motion depends on its mass m , frequency n and amplitude A as E= k(m)^(x)(n)^(y)(A)^(z) .Find the value of (2x+y+z) [Amplitude is distance]

A rod PQ of mass, area of cross section A, length l and young's modulus of elasticity Y is lying on a smooth table as shown in figure. A force Fis applied at P. Find (a) tension at a distance x from end P, (b) longitudinal stress at this point, (c) total change in length and (d) total strain the rod.

A student forgot Newton's formula for speed of sound but the knows there speed (v), pressure (p) and density (d) in the formula. He then start using dimensional analysis method to find the actual relation. upsilon = kp^(x)d^(y) Where k is a dimensionless constant. On the basis of above passage answer the following questions: The value of y is :

A student forgot Newton's formula for speed of sound but the knows there speed (v), pressure (p) and density (d) in the formula. He then start using dimensional analysis method to find the actual relation. upsilon = kp^(x)d^(y) Where k is a dimensionless constant. On the basis of above passage answer the following questions: The value of x is :